Chapter_05.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Modeling Non-Linearities\n",
    "\n",
    "linear models are simple to describe, implement and interpret\n",
    "\n",
    "But: have significant limitations in terms of predictive power\n",
    "\n",
    "Ridge Regression, Lasso, PCR and others try to reduce variance of estimates, but still model linearities\n",
    "\n",
    "**Non-Linear Models:**\n",
    "    - Polynomial Regression\n",
    "    \n",
    "    - Step Functions\n",
    "    \n",
    "    - Regression Splines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial Regression\n",
    "\n",
    "consider the following linear model\n",
    "\n",
    "$$ y_i = \\beta_0 + \\beta_1 x_i +\\epsilon_i $$\n",
    "\n",
    "a corresponding Polynomial models would be\n",
    "\n",
    "$$ y_i = \\beta_0 + \\beta_1 x_i + \\beta_2 x_i^2 +\\dots + \\beta_d x_i^d +\\epsilon_i $$\n",
    "\n",
    "Hence, Polynomial Regression allows for extremly non-linear curves\n",
    "\n",
    "### Computation of SE and CI for Polynomial Regression\n",
    "\n",
    "think of a model\n",
    "\n",
    "$$ \\hat{f}(x_0) = \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i + \\hat{\\beta}_2 x_i^2 + \\hat{\\beta}_3 x_i^3 $$\n",
    "\n",
    "estimation uses least squares and the variance is\n",
    "\n",
    "$$ Var(\\hat{f}(x_0)) = l_0'\\hat{C}l_0 $$\n",
    "\n",
    "Where $l_0' = (1,x_0,x_0^2,x_0^3)$ and $\\hat{C}$ is the $4 \\times 4$ covarite matrix.\n",
    "\n",
    "From least squares models we know that\n",
    "\n",
    "$$ SE = \\sqrt{Var(\\hat{f}(x_0))} $$\n",
    "\n",
    "$$ CI \\approx \\hat{f}(x_0) \\pm 2*SE $$\n",
    "\n",
    "### Logistic Polynomial Regression\n",
    "\n",
    "$$ Pr(y_i>250|x_i) = \\frac{exp\\{\\beta_0 + \\beta_1 x_i + \\beta_1 x_i + \\beta_2 x_i^2 +\\dots + \\beta_d x_i^d\\}} {1+exp\\{\\beta_0 + \\beta_1 x_i + \\beta_1 x_i + \\beta_2 x_i^2 +\\dots + \\beta_d x_i^d\\}} $$\n",
    "\n",
    "same estimation as in standard Logistic Regression approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step Functions\n",
    "\n",
    "**Idea:** \n",
    "break the range of $X$ into different bins $\\Rightarrow$ fit a different constant in each bin\n",
    "\n",
    "**Procedure:**\n",
    " 1. create cutpoints $c_1,c_2,\\dots,c_k$ in the range of $X$\n",
    " \n",
    " 2. create $k+1$ Dummy Variables $$C_{k-1}=I(C_{k-1}\\leq X < C_k)$$ with $C_i \\in \\{0,1\\}\\quad ,\\forall i$ and $\\sum_{i=1}^k C_i(x)=1 \\quad ,\\forall x$\n",
    " \n",
    " 3. fit a linear model using least squares $$y_i=\\beta_0+\\beta_1 C_1(x_i) + \\beta_2 C_2(x_i) + \\dots + \\beta_k C_k(x_i) + \\epsilon_i$$ \n",
    " \n",
    "again step functions can be performed using Logistic Regressions\n",
    " \n",
    "### What is the problem with Step Functions?\n",
    "\n",
    "unsless there are natural breakpoints, step functions can miss action (e.g. increasing linear trends)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basis Functions\n",
    "\n",
    "**Idea:** \n",
    "use any function/ transformation of $X$ in $b(X)$ such that\n",
    "\n",
    "$$y_i=\\beta_0+\\beta_1 b_1(x_i) + \\beta_2 b_2(x_i) + \\dots + \\beta_k b_k(x_i) + \\epsilon_i$$ \n",
    "\n",
    "Note: Polynomial Regression and Step-functions where special cases of basis functions\n",
    "\n",
    " * $b_j(x_i)=x_i^j$\n",
    " \n",
    " * $b_j(x_i)=I(C_j \\leq x_i <C_{j+1})$\n",
    " \n",
    "we can apply all tools available for least squares estimation, Inference, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression Splines\n",
    "\n",
    "**Idea:**\n",
    "piecewise polynomial regression with fitting the polynomial on different regions of $X$ (like a combination of polynomial regression and step functions)\n",
    "\n",
    "$$\n",
    "y_i= \n",
    "\\begin{cases}\n",
    "\\beta_{01}+\\beta_{11} x_i + \\beta_{21} x_i^2 + \\dots + \\beta_{d1} x_i^d + \\epsilon_i \\quad , x_i<c \\\\\n",
    "\\beta_{02}+\\beta_{12} x_i + \\beta_{22} x_i^2 + \\dots + \\beta_{d2} x_i^d + \\epsilon_i \\quad , x_i\\geq c \n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Thresholds are called knots, more knots $\\Rightarrow$ more flexible piecewise polynomial\n",
    "\n",
    "![](splines.png \"cubic regression spline with different constraints\")\n",
    "\n",
    "The figure above shows a cubic regression spline with different constraints. Top right, is unconstrained, while top left requires continuity at the threshold. The bottom left enforces smoothness at the threshold, by requiring first and second derivatives to be continuous (thus, we do not have the V-shaped look at the threshold as in top right).\n",
    "\n",
    "**Spline Basis Representation:**\n",
    "\n",
    "Let's stick with the example above, representing a cubic regression spline with knot (threshold) at $\\xi$. \n",
    "\n",
    "To ensure smoothness, we constraint our spline to be continuous at $f(\\xi)$, $f'(\\xi)$ and $f''(\\xi)$. This can be done by adding a *tunkated power basis* function per knot.\n",
    "\n",
    "$$ h(x,\\xi)=\n",
    "\\begin{cases}\n",
    "(x-\\xi)_+^3 \\quad, x>\\xi \\\\\n",
    "0 \\qquad, otherwise\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Thus the frist two derivates are continuous at $\\xi$ (due to the power of $3$). \n",
    "\n",
    "The Spline (bottom left) is respresented as:\n",
    "\n",
    "$$ y_i=\\beta_0 +\\beta_1 x_i +\\beta_2 x_i^2 +\\beta_3 x_i^3 +\\beta_4 h(x_i,\\xi) +\\epsilon_i $$\n",
    "\n",
    "**natural Spline**\n",
    "regression spline with additional boundary constraints (function is required to be linear at the boundary)\n",
    "\n",
    "### Where to place knots?\n",
    "\n",
    " - more knots $\\Rightarrow$ more flexible function\n",
    " \n",
    " - at points where the function needs to be flexible \n",
    " \n",
    " - *often place knots uniformly*\n",
    " \n",
    "### How many knots should we use?\n",
    "\n",
    "**apply CV:**\n",
    " 1. remove portion of data\n",
    " \n",
    " 2. fit spline with certain number on knots\n",
    " \n",
    " 3. make predictions\n",
    "\n",
    " 4. repeat until each set was used for training\n",
    " \n",
    " 5. calculate RSS\n",
    " \n",
    " 6. repeat with different number of knots and compare!\n",
    " \n",
    "### Comparing Polynomials and Splines\n",
    "\n",
    "Regression Splines often give superior results to polynomial regressions.\n",
    "\n",
    " - polynomials need high degree to be flexible\n",
    " \n",
    " - splines introduce flexibility by increasing knots and keep degree fixed\n",
    " \n",
    "**generally Regression Splines produce more stable estimates!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "Consider the following data generating process in which we have n observations and one covariate X covariates additional to a constant. $X \\sim N_p(0, \\sigma^2)$. $\\beta' = (1, 1.5, −1.5, 1.5)$ and the errors are drawn from a normal distribution $\\epsilon \\sim N (0, 1)$. The model is generated by $y_i = \\beta_0 + \\beta_1 x_i + \\beta_2 x_i^2 + \\beta_3 x_i^3 + \\epsilon_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "rm(list=ls())\n",
    "library(boot) # Bootstrap\n",
    "\n",
    "## DGP\n",
    "# Simulating OLS samples and plot the regression lines\n",
    "set.seed(123)\n",
    "# Two explanatory variables plus an intercept:\n",
    "N         <- 200\n",
    "X.1       <- rep(1, N)\n",
    "X.2      <- rnorm(N, mean=0, sd=1) # (pseudo) random numbers form a normal distr\n",
    "X         <- cbind(X.1, X.2,X.2^2,X.2^3)\n",
    "# Homoscedastic error term\n",
    "eps       <-rnorm(N,0,10)# \n",
    "beta.vec  <- c(1,1.5,-1.5,1.5)\n",
    "y         <- X %*% beta.vec + eps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Calculate the analytical standard errors for the polynomial specification above (as presented in the lecture) and use these to calculate the approximate confidence intervals as $2*SE$ for each value of $X$ you consider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table>\n",
       "<caption>A matrix: 4 × 1 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X.1</th><td> 0.6712096</td></tr>\n",
       "\t<tr><th scope=row>X.2</th><td> 0.1842706</td></tr>\n",
       "\t<tr><th scope=row></th><td>-0.7513726</td></tr>\n",
       "\t<tr><th scope=row></th><td> 1.7823084</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 1 of type dbl\n",
       "\\begin{tabular}{r|l}\n",
       "\tX.1 &  0.6712096\\\\\n",
       "\tX.2 &  0.1842706\\\\\n",
       "\t & -0.7513726\\\\\n",
       "\t &  1.7823084\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 1 of type dbl\n",
       "\n",
       "| X.1 |  0.6712096 |\n",
       "| X.2 |  0.1842706 |\n",
       "| <!----> | -0.7513726 |\n",
       "| <!----> |  1.7823084 |\n",
       "\n"
      ],
      "text/plain": [
       "    [,1]      \n",
       "X.1  0.6712096\n",
       "X.2  0.1842706\n",
       "    -0.7513726\n",
       "     1.7823084"
      ]
     },
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     "output_type": "display_data"
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BBAAAEEEGhf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mm+yaSpBWb59eFv9w4qpEDV/7ycSmPDw1\nkyacmIToZUmM5hP/9aajvVI5nEKAAAECBAgQIHAcAQnScYB8PbqABOkbzS7IovclaojcLyRO\nToy9JCm6T+LlmWjhysRVef+UsR/EDgkQIECAAAEC3RaQIHW7fbeldhKkr2d/cT7W9NivT9Q9\nRmMvN2a/GUp3WZKifl4vzWx0P5nxeqeN/UB2SIAAAQIECBDovoAEqfttvOU1lCDdSl5D6JK/\ntB+6ddF43+VBSKckKfqHJEXvurntuft4925vBAgQIECAAIGZE+hUgmQWu5m7fie+wjVFd12X\nb9yMM704s9+d3uZen4e2nnJzO/jodBnVRA8KAQIECBAgQIAAgUUBCZILYdIEHpMT+vvEeqbn\nPm5dnt92vyIrPSxTdj9EcnRcLisQIECAAAECBGZOQII0c00+8RWuBOlNm3GWmZ3ul7LfH29t\n4TEntMMf34xj2CcBAgQIECBAgAABAhsXcA/SUcM8e7Wlc6c9eOOkt+7h4gyry/1Gr0qCdGPu\nOXrCrd94R4AAAQIECBAgMAaBTt2DNAYPuxiDgATpKOLT85Jns7adYzBd3MWHWx5s1ObekOTo\ny4fargvHtV/7IUCAAAECBAgQuEWgUwmSIXa3tKs3EyBQw+vemqgpvjdcrm9t/wltz5/labN3\nW2j9R+xphz+04Z3aAQECBAgQIECAQKcFdnS6dio3bQKVIL1lHCedB77eO8nRpa31TzvUDj5k\nT5uXHI0D1j4IECBAgAABAh0XkCB1vIGnqHr3zLneIbGhBCkPULrDfNv9o7mw39Nr/cuuafPf\ndlJrn50iB6dKgAABAgQIECCwjQKG2G0jvkN/nUD1Hn0i8cmvW7rswyW5N+mJbe5bsmhXkp8d\niRMX2o5zkwzdtd9aHvjauzDD6e6SXqN6ttGv7m7zL81rvlIIECBAgAABAgQIDCcgQRrOyVqb\nL/DYHOKYvUfpFXpIEqDf67Xe/Y6eSlKhlCRHV/dbvxKrxMIrFlrvbzOcLnMzSIzKRyFAgAAB\nAgQIECAwjQLPzElXT8fJ03jyGzzn5DjtexM3JJ6ycl9fbe2MTNH96sxCdySz0f3JTa2dm2nu\n9qWL6LSPt7Zn5fo+EyBAgAABAgQIbLmAWey2nNwBuyRQzzo6cSnum9cXJO6a+I+Jv0rcUvLM\nou/MfN9/mB6i69I79B1z7fA7bvnSGwIECBAgQIAAAQIEOiswKz1IL0sLVk/ZIG7O+99OnJO4\npXwhPWnpNfq99Bodzmx0v6qn6BYabwgQIECAAAECkyjQqR6kSQSexXOahQTp7mnY+cSPJO6c\nqKSoepK+oRxqe96aBOmTebDrw7/hSwsIECBAgAABAgQmTUCCNGkt0oHzmYUE6c1pp2NOwjBo\nwy+1dmr1HCU5umiwzCsBAgQIECBAgMBEC3QqQTKL3URfa505uSelJo9KLM1Ad+x6ndp2PTTf\nHrmyHX7vsdfyDQECBAgQIECAAIHNEagZxBQCmylwQnb+m4m61+ijxztQr+14eG5Qen/G4NX9\nSQoBAgQIECBAgACBLRWQIG0p90we7BdT65qO+0XD1H5H631bEqR3DbOudQgQIECAAAECBAiM\nW0CCNG5R+1su8L358LzEsxIHln+x2vv3t7Y7E9w9uN96f7fa95YRIECAAAECBAgQIDAbAl2c\npOERaboaJvecYZswEzM8NBM0LOShR6cPu431CBAgQIAAAQIEtl2gU5M06EHa9uupkydwj9Tq\nzxOvTtT9R0OWxfuPPrSvta8MuYHVCBAgQIAAAQIECIxVQII0Vk47i8D9E/8j8beJn0qMUr6t\nGV43ipd1CRAgQIAAAQIExiwgQRoz6Izv7mmp/7sTNcnC0xMLiWFLLyte2G99EzQMK2Y9AgQI\nECBAgAABAh0V6MI9SC9N2xxO/Ox62uhgm7v3obanf2Nrd1jP9rYhQIAAAQIECBDYNoFO3YPk\nQbHbdh116sCvSG1+JPFdiTevp2a91s/03r1Pn9TalevZ3jYECBAgQIAAAQIExiEgQRqH4mzv\n40Wpfk3j/Z2Juu9onaX38EzxbXjdOvVsRoAAAQIECBAgMB4B9yCNx3FW9/LcVLyec/SUxLqT\no4/nQbK91su04BKkWb2Q1JsAAQIECBAgQIDAcoFpuwepnlP0u4lDiacur8io73Pv0ZPn255P\n5P6jq29q7U6jbm99AgQIECBAgACBbRdwD9K2N4ET2C6BmmnuhxK/krg28bjE2xJDlUqAdrW5\nf52p7U7OBiem1+iC3Hv0sH5beOWBdujFZ7T21aF2ZCUCBAgQIECAAAECmyTgHqRNgu3obn8j\n9frRxEsSNTHDfGLosqvteXW/tXtmXOcnMpzuxrz/lyOt98wT2nxG2SkECBAgQIAAAQIECBA4\nKjANQ+xq+NvBxBPX02iH2q5HHmpzR2o67/VsbxsCBAgQIECAAIGJFejUELuJVZ6xE5uGBOmP\n0ibvXW+7zLe5/5V47Xq3tx0BAgQIECBAgMDECkiQJrZppvfEJj1Bukdo6yGwj14PcXqNnpTe\no4O5B+nc9WxvGwIECBAgQIAAgYkWkCBNdPNM58lNeoL0xrAOPRnD8ia4uLUd6Tn6cGaqe+Xy\n5d4TIECAAAECBAh0RkCC1JmmnJyKTHKC9MAwZeK59pD1cM233T+Y3qMDB1o7ez3b24YAAQIE\nCBAgQGDiBSRIE99E03eCk5og3S6Ulyb+Yj2kGVJ35yRHX078h/VsbxsCBAgQIECAAIGpEOhU\ngpQZlxUCqwr8H1n6wUQ9DPZZq66xxsLP5jlHO9vcf2mt9/6XtvmXrbGqrwgQIECAAAECBAgQ\nIPB1ApPWg/SinN2RRD0Qdl3Pysp9R3+S+46uuL61/dmHQoAAAQIECBAg0F2BTvUgdbeZpqtm\nk5QgVUJU9xw9Y72ESYyenWF1N+X+o7p/SSFAgAABAgQIEOi2QKcSpHX1DnS7fWe+dtXj00us\n65lHSYp+otf6r+i3/jPm2qEPzLwmAAIECBAgQIAAgakSkCBNVXNtyckOhsRdM+rR8ryjX05m\n9TPpfvrBPe3Qn466vfUJECBAgAABAgQIbLeASRq2uwUm7/hnLp3StcOe2sVHn3X02lxM//5I\nW3jCnjYvORoWz3oECBAgQIAAAQITJaAHaaKaYyJOpnqQrkscHvZsnt/2/FaG1X1XhtVddEI7\n/A/Dbmc9AgQIECBAgAABApMmIEGatBbZ/vOpHqShe48yIcNPJTn60czr8Og5ydH2t54zIECA\nAAECBAgQ2JCABGlDfJ3cuBKkoe4/yj1HT0py9Ou55+j79rTDf9dJDZUiQIAAAQIECBCYKQH3\nIM1Ucw9V2Rpid9wEKcnRk3PxvC7rviD3HL1+qD1biQABAgQIECBAgMCEC0iQJryBtuH01hxi\nlwe/npmHwL4hF84l6Tn61d1t/mXbcI4OSYAAAQIECBAgQGBTBAyx2xTWqd5pJUj/tFoNDrVd\nj2xt5yWZjOHziQdnKm/POVoNyjICBAgQIECAAIGpFdCDNLVNt2knfqwhdr1+2/E7SYz+++Vt\n/nwPgd00fzsmQIAAAQIECBDYRgE9SNuIP6GHXnWIXe45ekoeAnvng23+Uee3dmhCz91pESBA\ngAABAgQIENiQgB6kDfF1cuNVe5CSHD2/33qvOaW1L3Sy1ipFgAABAgQIECBAIAJ6kFwGywV2\n5sO+xNfNYndz2/Odmc77PofbwacsX9l7AgQIECBAgAABAl0T0IPUtRbdWH2q9yidRV//oNhc\nJL/Qb+1PT2zt0xvbva0JECBAgAABAgQITLaAHqTJbp+tPrtKkKrc0oOUmesuaq3/0COt94yj\nX/mXAAECBAgQIECAQHcFJEjdbdv11KwmaKhybf1zQ2u3zcx1v5W3bzyhHfznWqYQIECAAAEC\nBAgQ6LKAIXZdbt3R61YJ0lcTh+fb7gfPtT3vz/ub59v8T46+K1sQIECAAAECBAgQmD4BCdL0\ntdlmnvHiDHZJjn6o13p/m/uO/tvH2/xFmbnu6s08qH0TIECAAAECBAgQmBQBQ+wmpSUm4zyq\nB+maJEevzusL5trBX56M03IWBAgQIECAAAECBLZGQA/S1jhPy1H2n704xK63a6G1v56Wk3ae\nBAgQIECAAAECBMYlIEEal2Q39nPmHRfnZmjtSJtfnKihG9VSCwIECBAgQIAAAQLDCUiQhnOa\nlbXOvFPbcVNVNtnRl2el0upJgAABAgQIECBAYCAgQRpIeC2B/ee23nyee3RTepIWEyUsBAgQ\nIECAAAECBGZJQII0S619/LqmBymj61rP8LrjW1mDAAECBAgQIECggwISpA426gaqdOa5bUfr\nt77hdRtAtCkBAgQIECBAgMD0CkiQprftxn3mO7PDfbdtbUem+daDNG5d+yNAgAABAgQIEJgK\nAQnSVDTTlpzkGTlK76zW25N7kPQgbQm5gxAgQIAAAQIECEyagARp0lpk+85nfx16X2sn9vUg\nbV8rODIBAgQIECBAgMC2CkiQtpV/og5+Zp3NSa13cu5BMsRuoprGyRAgQIAAAQIECGyVwK6t\nOpDjTLxAJUhf7bX+GbkHyRC7iW8uJ0iAAAECBAgQILAZAnqQNkN1OvdZQ+yuyW1IZ/Tbgh6k\n6WxDZ02AAAECBAgQILBBAQnSBgE7tHn1IF2THqT9uQdJD1KHGlZVCBAgQIAAAQIEhheQIA1v\n1fU1z8w839VzdNoOPUhdb2v1I0CAAAECBAgQOIaABOkYMDO4eP/tWzuQIXa9hbZDD9IMXgCq\nTIAAAQIECBAgkIeCQiCwJHDmndqOG+v9oTbvHiSXBQECBAgQIECAwEwKSJBmstlXrfT+u7Z2\nsL75WGt6kFYlspAAAQIECBAgQKDrAhKkrrfw8PU7886td6S1/oHzqxNJIUCAAAECBAgQIDCD\nAhKkGWz0Y1Q5CVJbyAx2htcdA8hiAgQIECBAgACB7gtIkLrfxsPUsK6DfbkHKa99w+uGEbMO\nAQIECBAgQIBAJwUkSJ1s1pErdUa22HGb1nb19CCNjGcDAgQIECBAgACB7ghIkLrTlhupST0k\ntp3Zeif09SBtxNG2BAgQIECAAAECUy4gQZryBhzT6d89+7nhtNZOzHOQ3IM0JlS7IUCAAAEC\nBAgQmD4BCdL0tdlmnPGDstPLMrxuvx6kzeC1TwIECBAgQIAAgWkRkCBNS0tt7nlekN1fmuRo\nv3uQNhfa3gkQIECAAAECBCZbQII02e2zVWeXRx+192V4XSZrWDDEbqvUHYcAAQIECBAgQGDi\nBCRIE9ckW35Cd80Raxa7S3vpQVpoO0zzveVN4IAECBAgQIAAAQKTIiBBmpSW2L7zqOF113y4\ntavSg3TyDj1I29cSjkyAAAECBAgQILDtAhKkbW+CbT+BmqDh0nNb219nogepFBQCBAgQIECA\nAIFZFZAgzWrL31rvxQkadrW5GmbX5ttB9yDdauMdAQIECBAgQIDAjAlIkGaswVdUd2c+PyDx\nvgytSw9Sv//m1q5bsY6PBAgQIECAAAECBGZGQII0M029akXvlaUnJS7N0LrqQbruaa0dWXVN\nCwkQIECAAAECBAjMgIAEaQYaeY0q1vC6zyS+WDPY9VvPDHZrYPmKAAECBAgQIECg+wISpO63\n8Vo1rAka8vyjzF/XejXEzv1Ha2n5jgABAgQIECBAoPMCEqTON/GaFVycwa7WWMizkJIkSZDW\n5PIlAQIECBAgQIBA1wUkSF1v4WPX74R8dZ/ELT1I/dY3xO7YXr4hQIAAAQIECBCYAYFdM1DH\nlVU8PQv2JvYkvpaoWdtuSMxaqdnrKkG+rCqee5DOSIJ0Zb1XCBAgQIAAAQIECMyqwKz0IFUy\n8AeJLyaql+RTiY8lKiGoJOkTif+UOCsxK6V6j6reB6rCmaBhf4bY6UEqDIUAAQIECBAgQGBm\nBWahB+kFad0XLrXwZ/L6vxKVCFRiVD1JNb31NyV+NPHUxLMTr0t0vVRP2pdureRiD5J7kG4F\n8Y4AAQIECBAgQGAGBbqeIH1P2rSSozz/tP1C4gOJ1UovCx+e+I3E/5u4IvGeRJfLvlTuq4MK\n1ix2mahBD9IAxCsBAgQIECBAgMBMCnR9iN2T0qqfTNTrsZKjavh+4p2JxyZqyNn3J7peqves\n7r9aKtWDtKAHacDhlQABAgQIECBAYCYFup4g3TetWkPqDg7Zul/Jepcnbj/k+tO82i09SJ9r\n7aRM03DCDtN8T3N7OncCBAgQIECAAIExXOsRZgAAHaBJREFUCHQ9Qfp8jM5L7B7Squ7LqaSq\nJnDoermlBymZ0v6q7EI7ZIhd11td/QgQIECAAAECBNYU6HqC9NrU/h6JP0s8eA2JwT1Ida9S\nelPan6+xble+uqUHaVfbvTh7X+Y6v6YrlVMPAgQIECBAgAABAusR6PokDTUb3dmJlyS+O3FV\n4spE3WtzfeK0RM1id6fEbROHEz+TeHei6+WWHqRU9H6JK9ONVCYKAQIECBAgQIAAAQIdF7hL\n6vf6RCVINSHD8kjHSft44tcTd0xsR3lmDlrndPIWHrwSxafX8ebbnlcdanOz0Gu2hbwORYAA\nAQIECBCYGYG51LR+l31oF2rc9R6kQRvVTHaLyUBeq9eoek9OSNSDY2+Z6jrvZ6mUwVLd++fn\n/V/NUuXVlQABAgQIECBAgMBqAl2/B2llnau+NYzss4nqNVqZHO3MspqooZKnLpeq5ymJ697e\n2q7cgHW/I613WZcrrG4ECBAgQIAAAQIEhhGYhQTpNoH4/xI1Q1slR8kJ2oWJ1cp9srDWe95q\nX3ZoWfUeVfnqhW33vWqK70PtoATpqIl/CRAgQIAAAQIEZlig60Psqpfk0kTdW1TJUd13c1Hi\nnYmXJ34hsRnlLtnp5YkajzlMqVn0qiwcfdn0f2sGuyrXJR6XAaOfPfXocMPFhf4hQIAAAQIE\nCBAgMKsCXU+QfjYNW8nRCxO/kTiQOC/xmsTzEycmfjox7vKp7PC7EruH3PE9s95vJ44Muf5G\nV7ulB6m1Hef3Wv/9G92h7QkQIECAAAECBAgQmHyBt+QUr06sTAQrQahepHSetEqiBuX+eVPL\nfmmwYItea8aPOu6wPU4bPa1vzw5qSvPMYDf33sxgt1k9aRs9T9sTIECAAAECBAhMvkCnZrHr\n+j1It8/19K7EYjKw7NqqyRmqh6eGwf1K4mmJWSqLM9il22j30QkaFvQgzVLrqysBAgQIECBA\ngMAxBbqeIH06NX90YrVZ6eqepMcn6r6k1yYuTMxKqXuQrrvv0Qka9sy3wyZomJWWV08CBAgQ\nIECAAIE1BbqeIL01ta/ekpclbreKRD049jGJujfpvyWekJiFstiDlIqen3F9n86Doa6ZhUqr\nIwECBAgQIECAAIHjCXQ9QXpVAD6SeE6inn30vYmV5Z+y4LGJmkHuJUtfZuRZp0v1IGWY4Y7z\nMkGD3qNON7XKESBAgAABAgQIjCLQ9QTp5mA8OPHKxGcS84nVygez8PzEm1f7soPLqgfpuswL\nUXV2/1EHG1iVCBAgQIAAAQIECAwjMExC+KDs6D7D7GyM62z1LHavyVQjr83sdTff3HZV75lC\ngAABAgQIECBAYL0C+dVycUbm+p126svK6a+nvkLHqcDKB7HWc4rKoHqaaprtKvVg2a6XvY9t\nO1Lnngkaut7S6keAAAECBAgQIDCSwDA9KiPtcMpW/rWc742JenjsLJV9j2i9k5cmaLh2liqu\nrgQIECBAgAABAgTWEpj1BGktmy5/t/cOrZe273++y5VUNwIECBAgQIAAAQKjCkiQRhXrxvr7\n9md8Xa/16oG5CgECBAgQIECAAAECSwISpNm8FPae0Xbs7Ld+ZrJTCBAgQIAAAQIECBAYCEiQ\nBhKz9bp3b+tnggo9SLPV7GpLgAABAgQIECBwPIFZm8VupcefZkE9KPVTK7/o8OeTUrfdp7Y2\nlx4kQ+w63NCqRoAAAQIECBAgMLrArCdI9ZDUWXtQ6r66TE5svRPSfShBGv2/GVsQIECAAAEC\nBAh0WMAQuw437jGqtreW72kt03zrQTqGkcUECBAgQIAAAQIzKiBBmr2GX+xB2tl6p6TqepBm\nr/3VmAABAgQIECBAYA0BCdIaOB39qnqQbuq1/t6FtkOC1NFGVi0CBAgQIECAAIH1CUiQ1uc2\nzVtVD1JN733aznZEgjTNLencCRAgQIAAAQIExi4gQRo76cTvcO9prR3IFN87+q1XiZJCgAAB\nAgQIECBAgMCSgARp9i6FfWe1dkNV+0g7pAdp9tpfjQkQIECAAAECBNYQkCCtgdPRr/ae1Xo3\nVt0OmqSho02sWgQIECBAgAABAusVkCCtV256t9t3m9ZurtP/h8WhdtNbEWdOgAABAgQIECBA\nYNwCEqRxi07+/vae3XbMt9b/2re3dnjyT9cZEiBAgAABAgQIENg6AQnS1llPypH2nbOYGPXc\nfzQpLeI8CBAgQIAAAQIEJkZAgjQxTbFlJ7I3CdJCv/UlSFtG7kAECBAgQIAAAQLTIiBBmpaW\nGt957ju79WpvEqTxmdoTAQIECBAgQIBARwQkSB1pyBGqsfeM1nb0PANpBDKrEiBAgAABAgQI\nzIqABGlWWvrWeu47o+3YaYjdrSDeESBAgAABAgQIEBgISJAGErPxujPVPGVv6+9uzSQNs9Hk\nakmAAAECBAgQIDCKgARpFK3pX3dvVeGU1vboQZr+xlQDAgQIECBAgACB8QtIkMZvOsl7XEyQ\nTmi9E9PwJmmY5JZybgQIECBAgAABAtsiIEHaFvZtO+i+OvJcayfrQdq2NnBgAgQIECBAgACB\nCRbYNcHn5tTGL1A9SAs7Wu/Uvh6k8evaIwECBAgQIECAwNQL6EGa+iYcqQLVg3R9r/X39k3S\nMBKclQkQIECAAAECBGZDQII0G+08qOXePCK27j06dWc7ct1goVcCBAgQIECAAAECBI4KSJBm\n60rYd3prBzLFd2+h7TBJw2y1vdoSIECAAAECBAgMISBBGgKpQ6vsPbO1G6o+C21egtShhlUV\nAgQIECBAgACB8QhIkMbjOC172Xd2691UJ3uzSRqmpc2cJwECBAgQIECAwBYKSJC2EHsCDnXy\nOa0tJkhvWRxqNwFn5BQIECBAgAABAgQIECCwQuCh+ZyZt+sRRZtabvfetvv7D7W56zf1KHZO\ngAABAgQIECAwSwL1O2z9Llu/00590YM09U04UgU+d/+W+RlM8T0SmpUJECBAgAABAgRmR8CD\nYmenrRdrevQZSItTfc9YzVWXAAECBAgQIECAwPEF9CAd36hTa/Rab296kDwDqVOtqjIECBAg\nQIAAAQLjEpAgjUtySvaT8XV5WGzfFN9T0l5OkwABAgQIECBAYGsFJEhb673tR6sepNxBJ0Ha\n9pZwAgQIECBAgAABApMoIEGaxFbZ1HPq1xA7CdKmGts5AQIECBAgQIDAtApIkKa15dZ53ulB\n2tc3xG6dejYjQIAAAQIECBDouoAEqestvKJ+SY72ptH1IK1w8ZEAAQIECBAgQIBACUiQZu86\nyD1IJmmYvWZXYwIECBAgQIAAgWEEJEjDKHVonaOTNLgHqUNNqioECBAgQIAAAQJjFJAgjRFz\nOnbVTw+S5yBNR1s5SwIECBAgQIAAga0WkCBttfg2Hu+S1nZmBrtTdrYj7kHaxnZwaAIECBAg\nQIAAgckVkCBNbtuM/cwel4fE1k4X2g4J0th17ZAAAQIECBAgQKALAhKkLrTikHWYuyVBmpcg\nDWlmNQIECBAgQIAAgdkSkCDNUHvvbLsXe5BuMs33DLW6qhIgQIAAAQIECIwiIEEaRWvK1+3l\nGUit9fuvbO3AlFfF6RMgQIAAAQIECBDYFAEJ0qawTuZOc+/RvpzZgYvrNiSFAAECBAgQIECA\nAIFvEJAgfQNJdxdUD1Km+Hb/UXebWM0IECBAgAABAgQ2KCBB2iDglG1eQ+yum7JzdroECBAg\nQIAAAQIEtkxAgrRl1Nt/oF7rJUHSg7T9LeEMCBAgQIAAAQIEJlVg16Se2IyeV2bi3pSyu/Z6\nY+ufmQN8LW9P3pSj2CkBAgQIECBAgMAkChza5JParN9hN/m0V9+9BGl1l61eOrhoN3V2uR9v\nR9qeozWrJEkhQIAAAQIECBAgME6B+XHubLv21duuAzvuNwicnyWLPT3f8M3GFlySzd+ReOfG\ndmNrAusSqD/C/E7iZYkrEgqBrRa4aw74vMSzEmbw3Gp9xyuBb088PPGi+qAQ2AaBH8wx64/j\nFyc2s1RydNlmHsC+CYxL4KPZUf1ioBDYDoETc9B+4oLtOLhjEojAhYm6Bo2YcDlsl8BP5MCX\nb9fBHZdABP6fpYAxpIBJGoaEshoBAgQIECBAgAABAt0XkCB1v43VkAABAgQIECBAgACBIQUk\nSENCWY0AAQIECBAgQIAAge4LSJC638ZqSIAAAQIECBAgQIDAkAISpCGhrEaAAAECBAgQIECA\nQPcFJEjdb2M1JECAAAECBAgQIEBgSAEJ0pBQViNAgAABAgQIECBAoPsCEqTut7EaEiBAgAAB\nAgQIECAwpIAEaUgoqxEgQIAAAQIECBAg0H0BTxbvfhvPp4qHul9NNZxQgSM5r4VEXYcKge0Q\nqJ9/hxN1HSoEtkOgrkE/A7dD3jEHAq6/gYRXAksCd8zrHA0C2yhw1208tkMTKAHXoOtgOwX2\n5OB32M4TcOyZFzgjAhUKAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIEJk1g56SdkPMZm0C17UMTFyQOJ76cUAiMW+C07PCcxL5VYneW\n3ZhYWe6QBRcl6vWLiUMJhcCoAudmgyck/nGNDUe51kZZd41D+mqGBM5NXde6Br8p36/2s7GW\n3ZBYSCwvrsHlGt4fS+CkfPHAxIWJupauTxxMrFZG/V3QNbiaomWdEbhbavLRRH9ZfDjv75hQ\nCIxT4Heys+XX2fL3r1vlQC/MskqIBusdzvvnrrKeRQTWEqjE/COJA2usNMq1Nsq6axzSVzMk\ncLxr8OxYDH7OrfZ69xVWrsEVID6uKvD9WXp1Yvk1VQnSs1dZe9TfBV2DqyBa1B2BXqryzkT9\nB/NvE9+ceGbixsSnEycnFALjEnhPdlS/pP7mKlHX3/LymHyoH+pvSjwgcUHizYla9hMJhcAw\nAqdnpcF1c6wEaZRrbZR1hzk/63RfYJhr8LFhqJ9tb0ms9vPxrGVMrsFlGN4eU6Cuk+p1/FTi\n5xP3TlRi9LFEXWvflxiUUX8XdA0O5Lx2VuDHU7P6D+XHVtTwmcdYvmI1HwkMLbAja34t8fYh\ntqghAfVD/crE8qG9c0vLP7tieT4qBL5B4MlZ8rlE/YyrISWrJUijXGujrJvDKQTaMNdgMT0v\nUdfpRfVhjeIaXAPHV18n8PZ8qmuqku/l5UH5UMtrpNCgjPK7oGtwoOa10wLvTe1uTtS41OWl\nhgPclLh0+ULvCWxA4Fuybf1Q/rUh9vGdS+u+fJV1X7r0XY3lVwgcS2BwDV2TFf7PxAcSqyVI\ng/WGudZGWfdY52X57AgMrpfjXYMl8vpE/bX/1PqwRhnsc5jrdY3d+KrjAvUHyfclKgla/kfG\nQbWrF6mGrA++e2/eD/u7oGtwoLjstcCV7gjsTlXun/jnxHUrqlVD7uo/oPslaj2FwEYF6lqr\nclniYYkaJvcDiUqcVpYaTlelfsCvLINl56/8wmcCywTqf/4vSdw98RfLlq98O8q1Nsq6K4/j\n8+wJDHsNlszg/8XVS/70xHMSj0ucmFheXIPLNbw/lkAl23Wt3CtxZMVKJ+TzbRNXJOq7UX8X\ndA0GbWXZtXKBz1MtUOOi64fxtceoxZezvP7DqbHPnzvGOhYTGFZgkCC9KBvcbdlG9YP8txPP\nTdQvFFVuc/Rl1Wuzrssqtz/64l8CqwrUvRwVxyujXGujrHu84/q++wLDXoM1ZKkS+S8lPpVY\n3ov08Xz+t4nBH4Zcg8FQNiTwvGx9WuL3lvYy6u+CrsFV+PUgrYIyxYvqP5Aq1f2/Whn8Inry\nal9aRmBEgQcsrf+FvD4+UbMk1utHE89J/FxiUNa6Nl2XAyWv4xAY5VobZd1xnJt9zIbAfVPN\n+v2qflF9ceJbE/WX/19O3CXxl4kzElVcg0cd/Ls+gadlsxckKvG+OFFlrWuqvv9y/ZMy+F1w\nrfVXrnt0yxn4Vw9Stxq5xptWOVbiOxiburJ79uhW/iUwmsBLs/olidclBtfelXn/D4mPJf5D\nomZvuiEx+H61a9N1GSBlbAKjXGujrDu2E7Sjzgt8MjWsYXWfTbx7WW2fn/f186561386UT8j\nXYNBUNYl8IPZ6tWJ6ql8YuKmRJW1rqn6fuX/c9daf+W6tf1MlNV+WZmJine0kvWX/LppfvCX\nqZXVHCz/6sovfCawDoF3ZZvXJAY/XAe7qOuwhqLsSdRfTqsMhnQOrsGjS4/+O1jmulyu4v16\nBUa51kZZd73nY7vZE/hiqvyGxPLkaKDwx0tvHrD06hocyHgdRaB6jf4oUX+UfESiRm4Myqi/\nC7oGB3LLXvUgLcPowNu636N+MA9+4VxZpVp+Y2LlBA4r1/OZwEYF6i9aVQZd98P8AL7q6Cb+\nJbAhgVGutVHW3dBJ2ZjAkoCfjS6FjQjU841+K/HsxKWJ705cnVheRv1d0M/B5XpL7/UgrYIy\n5Yvqrwj1V/szV9SjJma4Z+KyhCF2K3B8HFmgbjqua+k9idV+jtxjaY//tPQ6+OvWRUufl78M\nlr1v+ULvCaxTYJRrbZR113k6NptBgeekzvWzr4bZrSx+Nq4U8XlYgfp/bY3aqOTozxOPTKxM\njrJosYzyu6CfgwM1r50WeEpqV8Psaozz8vJz+VDL/9Xyhd4T2IDAP2bbuqbqJtHl5cJ8WEi8\ndfnCvL888fnEoFepvt6bqOEAdd+SHu0gKEMLfCBrrvYcpNrBKNfaKOsOfXJWnAmBY12DT03t\n62fjhxL1F/9BqfdvTtR3NSxqUFyDAwmvawn8eL6sa+dNicG9Qcda/ylL6w77u6Br8FiSlndG\noP7C8JFE9RK9OPHoxEuWPtd/VAqBcQl8R3ZU11nNmvgbibrW6odx/dJ6beK+ieWl/ppaP9yr\n56kS9e9J1C8YNRzggQmFwCgCde0cK0Ea5VobZd1Rzs+63Rc41jVYv7y+LVE/796e+L7EkxP/\nI1HLfj+xvLgGl2t4v5rA/iz8SqKun/rjY/UgrRanZHmVUX8XdA0edfNvxwVqeN1/T9Rf8es/\npoq/SZyTUAiMU+Dx2dk/JwbXWSU770rcObFa+TdZ+OXEYP16/8OrrWgZgeMIHOuX08Fmo1xr\no6w72L9XAmtdg6eH53cT9TNx8POu/pj0s4nVimtwNRXLBgI1S93gOlrrta67QRn1d0HX4EDO\na+cFTk0Nz0tIjDrf1NtewdvmDKoX6KQhzqSGmXxz4l6JmulOIbBZAqNca6Osu1nna7/dEzgh\nVbpP4twhquYaHALJKiMLjPK7oGtwZF4bECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgSmU2DndJ62syZAgACBjgqcl3o9JHFt4sYx1nF39vXExGmJq8a4X7siQIAAAQIECBAg\nQIDApgn8cfbcTzxqzEc4fWm/fzbm/dodAQIECHRMYEfH6qM6BAgQIECAAAECBAgQWLeABGnd\ndDYkQIAAAQIECBAgQKBrAru6ViH1IUCAAIHOCTwyNTor8cbEAxOPTNwm8cHEmxIHEyvL3bPg\n8Yl9ibcl/jFxrHK3fFFD+r4lcUXiHYnLE4Nyz7y5IPGFxN8MFi69Pjyvd0lcmvjI0jIvBAgQ\nIECAAAECBAgQGIvAH2cvK+9BqiToc4mfTiwkDiVqnYoPJM5ILC//MR/qu/nEl5be/8HS68p7\nkH4myyvBqv1+NnE4cSTx0kQvUaXuXxp896DFJUf/uXdebkpckahETCFAgAABAgQIECBAgMBY\nBY6VIFUC88XEsxKVsJyT+KtEJUI/nxiUH8mbWvYniZOWFn5HXmtWvFq+PEH67qVlf5vX2yWq\nnJp4XaLW/YHEoFQPU51D9UTNJfYkqpepkrWHJhQCBAgQIECAAAECBAiMXeBYCVIlLD+24mjf\nms+1vHqYBqV6emoo3ImDBUuvz85rrbs8QfrY0rKaWnx5OTkfaorx6rUa9CLV97+eqH38YuIV\nS++XJ2dZpBAgQIAAAQIECBAgQGB8AmslSPdZcZjqIaqE5X8uLd+/9Ln2sbLUPUvLE6QaElef\n/zlx31WiepXq+9snBqV6jf53YjAk7y15v2PwpVcCBAgQ6IaASRq60Y5qQYAAgVkQqJ6h5eXm\npQ+DJGWQQK32INganleJzaDUxAxV6rWSnmOVb84Xg/3V9tUT9Y5ElcE9UUc/+ZcAAQIEOiEg\nQepEM6oEAQIEZkKg7gFaq1y79GUNkVtZaqjcIJGq7wbJ1d/k/a/VgmOUD61Y/pxln1+c909a\n9tlbAgQIEOiAgASpA42oCgQIECCwKFDTbNescvdYxeNOWbZ72fJ/yfsaQndm4q3Llg/ePjhv\naja7A4MFef2RxBMTNSNeJVvPSNSy+qwQIECAAAECBAgQIEBg7AJ/nD1W4vKoZXt+09Kyusdo\neakkpdZ927KFdV9Q9TQ9cNmyevubiVp3+SQNb15a9vi8Li/3yocaTldD7wZJ1Tfn/dcSn0mc\nltibuDJRy+o7hQABAgQIECBAgAABAmMX2GiCdMec0ecTNdzu3yUem6jnItWsdIcTyxOkb8nn\n6nGq+KXEYxLPTVTvUq17fqLKrsTfJyrBqv0NyhPyppbVd7WOQoAAAQIECBAgQIAAgbEKbDRB\nqpOpxKaGzdWDYiuBqckdLkrUcLnlCVI+Lg7He2deazhdrVtRPUM/kBiUi/Omlv/+YMGy18H5\nXrxsmbcECBAgQIAAAQIECBCYOIEaBne3Ic+qpgy/f+JOiZ1DbmM1AgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQITIHA\n/w/1lFF3HG/b6gAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Estimated Model vs True DGP”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PoRaDygW+v+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\nuxsrpjzmuxSio9S97qvztF9sFgEEEEAAAQQQQACBjgnQgtQx6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AAQQQQAABBBBA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\nAAIIIIAAAj0g8P8Bf8y42tVZQ60AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Estimated Model with analytical CI”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## computing SE and CI by relying on 2*SE\n",
    "# Solving for beta hat\n",
    "beta.hat <- solve(t(X) %*% X) %*% t(X) %*% y\n",
    "beta.hat\n",
    "x.grid<-sort(X.2) #\n",
    "true_model<-beta.vec[1]+beta.vec[2]*x.grid+beta.vec[3]*x.grid^2+beta.vec[4]*x.grid^3\n",
    "estim_model<-beta.hat[1]+beta.hat[2]*x.grid+beta.hat[3]*x.grid^2+beta.hat[4]*x.grid^3\n",
    "plot(estim_model,main=\"Estimated Model vs True DGP\",type=\"l\")\n",
    "lines(true_model,type=\"l\",lty=1,col=\"red\")\n",
    "y.hat<- X %*% beta.hat \n",
    "eps.hat<-y-X %*% beta.hat\n",
    "se<-(t(eps.hat)%*%(eps.hat))/(N-5)\n",
    "cov<-se[1]*solve(t(X) %*% X)\n",
    "new_data<-X[order(X[,2]),]\n",
    "var<-c()\n",
    "for(i in 1:N)\n",
    "{\n",
    "  var[i]=t(new_data[i,])%*%cov%*%(new_data[i,])\n",
    "}\n",
    "d<-2*(sqrt(var))\n",
    "estim<-beta.hat[1]+beta.hat[2]*new_data[,2]+beta.hat[3]*new_data[,2]^2+beta.hat[4]*new_data[,2]^3\n",
    "conf_low<-estim-d\n",
    "conf_high<-estim+d\n",
    "plot(estim,main=\"Estimated Model with analytical CI\",type=\"l\")\n",
    "lines(conf_low,lty=2,col=\"red\")\n",
    "lines(conf_high,lty=2,col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Calculate the naive bootstrap confidence intervals for B bootstrap draws from the original data, such that the nominal coverage for the two methods is the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ggAACCCCAAALJFsgHuWJn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\nECBAgAABAgQIEPgHAj8nonxpoQEAhAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## computing Bootstraped CI's\n",
    "B=200\n",
    "b_sample<-matrix(NA,N,B)\n",
    "beta.hat<-matrix(NA,length(X),B)\n",
    "data<-cbind(y,X)\n",
    "function_B<-matrix(NA,length(x.grid),B)\n",
    "for(i in 1:B)\n",
    "{\n",
    "  XB<- data[sample(nrow(data),replace=T, N), ]\n",
    "  beta.hat<-solve(t(XB[,2:5]) %*% XB[,2:5]) %*% t(XB[,2:5]) %*%XB[,1]\n",
    "  function_B[,i]<-beta.hat[1]+beta.hat[2]*x.grid+beta.hat[3]*x.grid^2+beta.hat[4]*x.grid^3\n",
    "}\n",
    "#plot(function_B[,1])\n",
    "#plot(function_B[,2])\n",
    "sorted<-t(apply(function_B,1,sort))\n",
    "# Calculate the empirical quantiles\n",
    "conf_highB<-sorted[,195]\n",
    "conf_lowB<-sorted[,5]\n",
    "plot(estim,type=\"l\",lty=3)\n",
    "lines(conf_highB)\n",
    "lines(conf_lowB)\n",
    "lines(conf_low,lty=2,col=\"red\")\n",
    "lines(conf_high,lty=2,col=\"blue\")\n",
    "lines(true_model,col=\"green\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Calculate the coverage probability at four different values of X, chosen by you."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability of Bootstrap:  1'</span>"
      ],
      "text/latex": [
       "'Coverage Probability of Bootstrap:  1'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability of Bootstrap:  1'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability of Bootstrap:  1\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability of Parametric:  1'</span>"
      ],
      "text/latex": [
       "'Coverage Probability of Parametric:  1'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability of Parametric:  1'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability of Parametric:  1\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## computing Coverage Probabilities\n",
    "cov_prob_B<-true_model>conf_lowB&true_model<conf_highB\n",
    "paste('Coverage Probability of Bootstrap: ', sum(cov_prob_B)/length(x.grid))\n",
    "cov_prob_A<-true_model>conf_low&true_model<conf_high\n",
    "paste('Coverage Probability of Parametric: ', sum(cov_prob_A)/length(x.grid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Calculate the interval length at four different values of X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'The number of times the bootstrapped interval length is larger than the analytical one'"
      ],
      "text/latex": [
       "'The number of times the bootstrapped interval length is larger than the analytical one'"
      ],
      "text/markdown": [
       "'The number of times the bootstrapped interval length is larger than the analytical one'"
      ],
      "text/plain": [
       "[1] \"The number of times the bootstrapped interval length is larger than the analytical one\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "123"
      ],
      "text/latex": [
       "123"
      ],
      "text/markdown": [
       "123"
      ],
      "text/plain": [
       "[1] 123"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## comupting interval length\n",
    "int_lengthB<-conf_highB-conf_lowB\n",
    "int_length<-conf_high-conf_low\n",
    "paste('The number of times the bootstrapped interval length is larger than the analytical one:')\n",
    "sum(int_lengthB/int_length>1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Simulation Study**\n",
    "\n",
    "Evaluate the two types of confidence intervals above along two dimensions: interval length and coverage probability.\n",
    "\n",
    "a) Calculate both for a small simulation study of 100 repetitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.978'</span>"
      ],
      "text/latex": [
       "'Coverage Probability, analytical standard errors:      0.978'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.978'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability, analytical standard errors:      0.978\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.831'</span>"
      ],
      "text/latex": [
       "'Coverage Probability:                                                   0.831'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.831'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability:                                                   0.831\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            5.4'</span>"
      ],
      "text/latex": [
       "'Interval length ratio sum, if >0.5*N:                            5.4'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            5.4'</span>"
      ],
      "text/plain": [
       "[1] \"Interval length ratio sum, if >0.5*N:                            5.4\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      5.12697604381123'</span>"
      ],
      "text/latex": [
       "'avg Interval length:                                                      5.12697604381123'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      5.12697604381123'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length:                                                      5.12697604381123\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                4.14725457615847'</span>"
      ],
      "text/latex": [
       "'avg Interval length (B):                                                4.14725457615847'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                4.14725457615847'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length (B):                                                4.14725457615847\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Simulation Study to check different methods given a certain DGP process\n",
    "data.conf<-function(model,N)\n",
    "{\n",
    "  ## Simulating OLS samples and plot the regression lines\n",
    "  #set.seed(123)\n",
    "  # Two explanatory variables plus an intercept:\n",
    "  #N         <- 200\n",
    "  X.1       <- rep(1, N)\n",
    "  X.2      <- rnorm(N, mean=0, sd=1) #(pseudo) random numbers form a normal distr\n",
    "  X         <- cbind(X.1, X.2,X.2^2,X.2^3)\n",
    "  # Error term\n",
    "  if(model==1)\n",
    "  {\n",
    "    eps       <-rnorm(N,0,10)# \n",
    "  }\n",
    "  if(model==2)\n",
    "  {\n",
    "    eps       <-rgamma(N,0.1,0.01)\n",
    "    eps<-scale(eps, scale = FALSE)\n",
    "  }\n",
    "  if(model==3)\n",
    "  {\n",
    "    eps       <-(X.2^2)*rnorm(N,0,10)# \n",
    "  }\n",
    "  ## Different distribution\n",
    "  if(model==4)\n",
    "  {\n",
    "    # Sample N random uniforms U\n",
    "    U =runif(N)\n",
    "    # Variable to store the samples from the mixture distribution                                             \n",
    "    eps = rep(NA,N)\n",
    "    # Sampling from the mixture\n",
    "    for(i in 1:N){\n",
    "      if(U[i]<.3){\n",
    "        eps[i] = rnorm(1,-5.9,1)\n",
    "      }else if(U[i]<.8){\n",
    "        eps[i] = rnorm(1,4.1,1)\n",
    "      }else{\n",
    "        eps[i] = rnorm(1,-1.9,.1)\n",
    "      }\n",
    "    }\n",
    "  }\n",
    "  # Density plot of the random samples\n",
    "  #plot(density(eps),main=\"Density Estimate of the Mixture Model\")\n",
    "  ####################################################################\n",
    "  if(model==5)\n",
    "  {\n",
    "    eps       <-  rt(N, df=1)# \n",
    "  }\n",
    "  \n",
    "  #plot(density(eps),main=\"Density Estimate of the t-distribution\")\n",
    "  \n",
    "  \n",
    "  if(model==6)\n",
    "  {\n",
    "    # Sample N random uniforms U\n",
    "    \n",
    "    # Variable to store the samples from the mixture distribution                                             \n",
    "    eps =  runif(N,-1,1)\n",
    "    # Sampling from the mixture\n",
    "  }\n",
    "  \n",
    "  ## Heteroscedastic error term\n",
    "  beta.vec  <- c(1,1.5,-1.5,1.5)\n",
    "  y         <- X %*% beta.vec + eps\n",
    "  # Solving for beta hat\n",
    "  beta.hat <- solve(t(X) %*% X) %*% t(X) %*% y\n",
    "  beta.hat\n",
    "  x.grid<-sort(X.2) #seq(min(X.2),max(X.2),le=N)\n",
    "  true_model<-beta.vec[1]+beta.vec[2]*x.grid+beta.vec[3]*x.grid^2+beta.vec[4]*x.grid^3\n",
    "  estim_model<-beta.hat[1]+beta.hat[2]*x.grid+beta.hat[3]*x.grid^2+beta.hat[4]*x.grid^3\n",
    "  #plot(estim_model,type=\"l\")\n",
    "  #lines(true_model,type=\"l\",lty=1,col=\"red\")\n",
    "  #Calculate the covariance matrix\n",
    "  #calculate the fitted values\n",
    "  y.hat<- X %*% beta.hat \n",
    "  eps.hat<-y-X %*% beta.hat\n",
    "  #calculate the covariance matrix\n",
    "  se<-(t(eps.hat)%*%(eps.hat))/(N-5)\n",
    "  cov<-se[1]*solve(t(X) %*% X)\n",
    "  new_data<-X[order(X[,2]),]\n",
    "  #new_data<-x.grid\n",
    "  var<-c()\n",
    "  for(i in 1:N)\n",
    "  {\n",
    "    var[i]=t(new_data[i,])%*%cov%*%(new_data[i,])\n",
    "  }\n",
    "  d<-2*(sqrt(var))\n",
    "  estim<-beta.hat[1]+beta.hat[2]*new_data[,2]+beta.hat[3]*new_data[,2]^2+beta.hat[4]*new_data[,2]^3\n",
    "  conf_low<-estim-d\n",
    "  conf_high<-estim+d\n",
    "  #plot(estim,type=\"l\")\n",
    "  #lines(conf_low,lty=2,col=\"red\")\n",
    "  #lines(conf_high,lty=2,col=\"blue\")\n",
    "  ## Bootstrapped confidence intervals\n",
    "  B=N\n",
    "  b_sample<-matrix(NA,N,B)\n",
    "  beta.hat<-matrix(NA,length(X),B)\n",
    "  data<-cbind(y,X)\n",
    "  function_B<-matrix(NA,length(x.grid),B)\n",
    "  \n",
    "  for(i in 1:B)\n",
    "  {\n",
    "    XB<- data[sample(nrow(data),replace=T, N), ]\n",
    "    beta.hat<-solve(t(XB[,2:5]) %*% XB[,2:5]) %*% t(XB[,2:5]) %*%XB[,1]\n",
    "    function_B[,i]<-beta.hat[1]+beta.hat[2]*x.grid+beta.hat[3]*x.grid^2+beta.hat[4]*x.grid^3\n",
    "  }\n",
    "  #plot(function_B[,1])\n",
    "  #plot(function_B[,2])\n",
    "  sorted<-t(apply(function_B,1,sort)) \n",
    "  # Calculate the empirical quantiles\n",
    "  conf_highB<-sorted[,B*0.95]\n",
    "  conf_lowB<-sorted[,B*0.05]\n",
    "  ###########################################\n",
    "  #plot(estim,type=\"l\",lty=3)\n",
    "  #lines(conf_highB)\n",
    "  #lines(conf_lowB)\n",
    "  #lines(conf_low,lty=2,col=\"red\")\n",
    "  #lines(conf_high,lty=2,col=\"blue\")\n",
    "  #lines(true_model,col=\"green\")\n",
    "  ## Calculate the coverage probabilities\n",
    "  cov_prob_B<-true_model>conf_lowB&true_model<conf_highB\n",
    "  ratio1_B= sum(cov_prob_B)/length(x.grid)\n",
    "  cov_prob_A<-true_model>conf_low&true_model<conf_high\n",
    "  ratio1=sum(cov_prob_A)/length(x.grid)\n",
    "  ## Calculate interval length\n",
    "  int_lengthB<-conf_highB-conf_lowB\n",
    "  int_length<-conf_high-conf_low\n",
    "  ratio2=sum(int_lengthB/int_length>1)\n",
    "  ratio2_int=mean(int_length)\n",
    "  ratioB_int=mean(int_lengthB)\n",
    "  return(list(ratio2=ratio2,ratio1_B=ratio1_B,ratio1=ratio1,ratio2_int=ratio2_int,ratioB_int=ratioB_int,conf_high=conf_high,conf_low=conf_low,conf_highB=conf_highB,conf_lowB=conf_lowB,true_model=true_model,estim=estim))\n",
    "}\n",
    "##########\n",
    "reps<-5\n",
    "result_1<-replicate(reps,data.conf(model=1,N=200)$ratio1)\n",
    "result_1B<-replicate(reps,data.conf(model=1,N=200)$ratio1_B)\n",
    "result_2<-replicate(reps,data.conf(model=1,N=200)$ratio2)\n",
    "result_int<-replicate(reps,data.conf(model=1,N=200)$ratio2_int)\n",
    "result_int_B<-replicate(reps,data.conf(model=1,N=200)$ratioB_int)\n",
    "#conf_highB<-replicate(reps,data.conf(model=1,N=200)$conf_highB)\n",
    "#conf_lowB<-replicate(reps,data.conf(model=1,N=200)$conf_lowB)\n",
    "#conf_low<-replicate(reps,data.conf(model=1,N=200)$conf_low)\n",
    "#conf_high<-replicate(reps,data.conf(model=1,N=200)$conf_high)\n",
    "#true_model<-replicate(reps,data.conf(model=1,N=200)$true_model)\n",
    "#estim<-replicate(reps,data.conf(model=1,N=200)$estim)\n",
    "#plot(estim,type=\"l\",lty=3)\n",
    "#  lines(conf_highB)\n",
    "#  lines(conf_lowB)\n",
    "#  lines(conf_low,lty=2,col=\"red\")\n",
    "#  lines(conf_high,lty=2,col=\"blue\")\n",
    "#  lines(true_model,col=\"green\")\n",
    "# cov.prob, analytical standard errors\n",
    "paste('Coverage Probability, analytical standard errors:     ', mean(result_1))\n",
    "# cov_ probability, \n",
    "paste('Coverage Probability:                                                  ',mean(result_1B))\n",
    "# interval length ratio sum, if >0.5*N: \n",
    "paste('Interval length ratio sum, if >0.5*N:                           ',mean(result_2))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length:                                                     ',mean(result_int))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length (B):                                               ',mean(result_int_B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) How could you change the data-generating process to give a competitive advantage to the bootstrap?\n",
    "Suggest two changes and check each in a simulation study."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.949'</span>"
      ],
      "text/latex": [
       "'Coverage Probability, analytical standard errors:      0.949'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.949'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability, analytical standard errors:      0.949\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.95'</span>"
      ],
      "text/latex": [
       "'Coverage Probability:                                                   0.95'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.95'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability:                                                   0.95\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            35.6'</span>"
      ],
      "text/latex": [
       "'Interval length ratio sum, if >0.5*N:                            35.6'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            35.6'</span>"
      ],
      "text/plain": [
       "[1] \"Interval length ratio sum, if >0.5*N:                            35.6\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      15.4348623029568'</span>"
      ],
      "text/latex": [
       "'avg Interval length:                                                      15.4348623029568'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      15.4348623029568'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length:                                                      15.4348623029568\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                12.7946411942827'</span>"
      ],
      "text/latex": [
       "'avg Interval length (B):                                                12.7946411942827'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                12.7946411942827'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length (B):                                                12.7946411942827\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## for the  gamma\n",
    "result_1<-replicate(reps,data.conf(model=2,N=200)$ratio1)\n",
    "result_1B<-replicate(reps,data.conf(model=2,N=200)$ratio1_B)\n",
    "result_2<-replicate(reps,data.conf(model=2,N=200)$ratio2)\n",
    "result_int<-replicate(reps,data.conf(model=2,N=200)$ratio2_int)\n",
    "result_int_B<-replicate(reps,data.conf(model=2,N=200)$ratioB_int)\n",
    "#conf_highB<-replicate(reps,data.conf(model=2,N=200)$conf_highB)\n",
    "#conf_lowB<-replicate(reps,data.conf(model=2,N=200)$conf_lowB)\n",
    "#conf_low<-replicate(reps,data.conf(model=2,N=200)$conf_low)\n",
    "#conf_high<-replicate(reps,data.conf(model=2,N=200)$conf_high)\n",
    "#true_model<-replicate(reps,data.conf(model=2,N=200)$true_model)\n",
    "#estim<-replicate(reps,data.conf(model=2,N=200)$estim)\n",
    "#plot(estim,type=\"l\",lty=3)\n",
    "#  lines(conf_highB)\n",
    "#  lines(conf_lowB)\n",
    "#  lines(conf_low,lty=2,col=\"red\")\n",
    "#  lines(conf_high,lty=2,col=\"blue\")\n",
    "#  lines(true_model,col=\"green\")\n",
    "# cov.prob, analytical standard errors\n",
    "paste('Coverage Probability, analytical standard errors:     ', mean(result_1))\n",
    "# cov_ probability, \n",
    "paste('Coverage Probability:                                                  ',mean(result_1B))\n",
    "# interval length ratio sum, if >0.5*N: \n",
    "paste('Interval length ratio sum, if >0.5*N:                           ',mean(result_2))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length:                                                     ',mean(result_int))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length (B):                                               ',mean(result_int_B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.897'</span>"
      ],
      "text/latex": [
       "'Coverage Probability, analytical standard errors:      0.897'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.897'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability, analytical standard errors:      0.897\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.971'</span>"
      ],
      "text/latex": [
       "'Coverage Probability:                                                   0.971'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.971'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability:                                                   0.971\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            100.2'</span>"
      ],
      "text/latex": [
       "'Interval length ratio sum, if >0.5*N:                            100.2'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            100.2'</span>"
      ],
      "text/plain": [
       "[1] \"Interval length ratio sum, if >0.5*N:                            100.2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      8.53708632304374'</span>"
      ],
      "text/latex": [
       "'avg Interval length:                                                      8.53708632304374'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      8.53708632304374'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length:                                                      8.53708632304374\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                7.90607309765732'</span>"
      ],
      "text/latex": [
       "'avg Interval length (B):                                                7.90607309765732'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                7.90607309765732'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length (B):                                                7.90607309765732\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## For the heteroscedastic errors\n",
    "result_1<-replicate(reps,data.conf(model=3,N=200)$ratio1)\n",
    "result_1B<-replicate(reps,data.conf(model=3,N=200)$ratio1_B)\n",
    "result_2<-replicate(reps,data.conf(model=3,N=200)$ratio2)\n",
    "result_int<-replicate(reps,data.conf(model=3,N=200)$ratio2_int)\n",
    "result_int_B<-replicate(reps,data.conf(model=3,N=200)$ratioB_int)\n",
    "#conf_highB<-replicate(reps,data.conf(model=3,N=200)$conf_highB)\n",
    "#conf_lowB<-replicate(reps,data.conf(model=3,N=200)$conf_lowB)\n",
    "#conf_low<-replicate(reps,data.conf(model=3,N=200)$conf_low)\n",
    "#conf_high<-replicate(reps,data.conf(model=3,N=200)$conf_high)\n",
    "#true_model<-replicate(reps,data.conf(model=3,N=200)$true_model)\n",
    "#estim<-replicate(reps,data.conf(model=3,N=200)$estim)\n",
    "#plot(estim,type=\"l\",lty=3)\n",
    "#  lines(conf_highB)\n",
    "#  lines(conf_lowB)\n",
    "#  lines(conf_low,lty=2,col=\"red\")\n",
    "#  lines(conf_high,lty=2,col=\"blue\")\n",
    "#  lines(true_model,col=\"green\")\n",
    "# cov.prob, analytical standard errors\n",
    "paste('Coverage Probability, analytical standard errors:     ', mean(result_1))\n",
    "# cov_ probability, \n",
    "paste('Coverage Probability:                                                  ',mean(result_1B))\n",
    "# interval length ratio sum, if >0.5*N: \n",
    "paste('Interval length ratio sum, if >0.5*N:                           ',mean(result_2))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length:                                                     ',mean(result_int))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length (B):                                               ',mean(result_int_B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note: for Heteroskedastic errors Bootstrapped CI's performes better\n",
    "\n",
    "**in all other cases, the analytical standard error/ CI is preferable**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.943'</span>"
      ],
      "text/latex": [
       "'Coverage Probability, analytical standard errors:      0.943'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      0.943'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability, analytical standard errors:      0.943\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.811'</span>"
      ],
      "text/latex": [
       "'Coverage Probability:                                                   0.811'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.811'</span>"
      ],
      "text/plain": [
       "[1] \"Coverage Probability:                                                   0.811\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            3.2'</span>"
      ],
      "text/latex": [
       "'Interval length ratio sum, if >0.5*N:                            3.2'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            3.2'</span>"
      ],
      "text/plain": [
       "[1] \"Interval length ratio sum, if >0.5*N:                            3.2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      2.25281913962345'</span>"
      ],
      "text/latex": [
       "'avg Interval length:                                                      2.25281913962345'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      2.25281913962345'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length:                                                      2.25281913962345\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                1.81301460357552'</span>"
      ],
      "text/latex": [
       "'avg Interval length (B):                                                1.81301460357552'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                1.81301460357552'</span>"
      ],
      "text/plain": [
       "[1] \"avg Interval length (B):                                                1.81301460357552\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## For the mixture model\n",
    "result_1<-replicate(reps,data.conf(model=4,N=200)$ratio1)\n",
    "result_1B<-replicate(reps,data.conf(model=4,N=200)$ratio1_B)\n",
    "result_2<-replicate(reps,data.conf(model=4,N=200)$ratio2)\n",
    "result_int<-replicate(reps,data.conf(model=4,N=200)$ratio2_int)\n",
    "result_int_B<-replicate(reps,data.conf(model=4,N=200)$ratioB_int)\n",
    "#conf_highB<-replicate(reps,data.conf(model=4,N=200)$conf_highB)\n",
    "#conf_lowB<-replicate(reps,data.conf(model=4,N=200)$conf_lowB)\n",
    "#conf_low<-replicate(reps,data.conf(model=4,N=200)$conf_low)\n",
    "#conf_high<-replicate(reps,data.conf(model=4,N=200)$conf_high)\n",
    "#true_model<-replicate(reps,data.conf(model=4,N=200)$true_model)\n",
    "#estim<-replicate(reps,data.conf(model=4,N=200)$estim)\n",
    "#plot(estim,type=\"l\",lty=3)\n",
    "#  lines(conf_highB)\n",
    "#  lines(conf_lowB)\n",
    "#  lines(conf_low,lty=2,col=\"red\")\n",
    "#  lines(conf_high,lty=2,col=\"blue\")\n",
    "#  lines(true_model,col=\"green\")\n",
    "# cov.prob, analytical standard errors\n",
    "paste('Coverage Probability, analytical standard errors:     ', mean(result_1))\n",
    "# cov_ probability, \n",
    "paste('Coverage Probability:                                                  ',mean(result_1B))\n",
    "# interval length ratio sum, if >0.5*N: \n",
    "paste('Interval length ratio sum, if >0.5*N:                           ',mean(result_2))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length:                                                     ',mean(result_int))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length (B):                                               ',mean(result_int_B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      1'</span>"
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      "text/latex": [
       "'Coverage Probability, analytical standard errors:      1'"
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      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability, analytical standard errors:      1'</span>"
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      "text/plain": [
       "[1] \"Coverage Probability, analytical standard errors:      1\""
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      "text/html": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.901'</span>"
      ],
      "text/latex": [
       "'Coverage Probability:                                                   0.901'"
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      "text/markdown": [
       "<span style=white-space:pre-wrap>'Coverage Probability:                                                   0.901'</span>"
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      "text/plain": [
       "[1] \"Coverage Probability:                                                   0.901\""
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      "text/html": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            1'</span>"
      ],
      "text/latex": [
       "'Interval length ratio sum, if >0.5*N:                            1'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Interval length ratio sum, if &gt;0.5*N:                            1'</span>"
      ],
      "text/plain": [
       "[1] \"Interval length ratio sum, if >0.5*N:                            1\""
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     },
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     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      0.289316576943655'</span>"
      ],
      "text/latex": [
       "'avg Interval length:                                                      0.289316576943655'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length:                                                      0.289316576943655'</span>"
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       "[1] \"avg Interval length:                                                      0.289316576943655\""
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     },
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      "text/html": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                0.238589305785196'</span>"
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      "text/latex": [
       "'avg Interval length (B):                                                0.238589305785196'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'avg Interval length (B):                                                0.238589305785196'</span>"
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       "[1] \"avg Interval length (B):                                                0.238589305785196\""
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   "source": [
    "## For the t distribution\n",
    "result_1<-replicate(reps,data.conf(model=6,N=200)$ratio1)\n",
    "result_1B<-replicate(reps,data.conf(model=6,N=200)$ratio1_B)\n",
    "result_2<-replicate(reps,data.conf(model=6,N=200)$ratio2)\n",
    "result_int<-replicate(reps,data.conf(model=6,N=200)$ratio2_int)\n",
    "result_int_B<-replicate(reps,data.conf(model=6,N=200)$ratioB_int)\n",
    "#conf_highB<-replicate(reps,data.conf(model=6,N=200)$conf_highB)\n",
    "#conf_lowB<-replicate(reps,data.conf(model=6,N=200)$conf_lowB)\n",
    "#conf_low<-replicate(reps,data.conf(model=6,N=200)$conf_low)\n",
    "#conf_high<-replicate(reps,data.conf(model=6,N=200)$conf_high)\n",
    "#true_model<-replicate(reps,data.conf(model=6,N=200)$true_model)\n",
    "#estim<-replicate(reps,data.conf(model=6,N=200)$estim)\n",
    "#plot(estim,type=\"l\",lty=3)\n",
    "#  lines(conf_highB)\n",
    "#  lines(conf_lowB)\n",
    "#  lines(conf_low,lty=2,col=\"red\")\n",
    "#  lines(conf_high,lty=2,col=\"blue\")\n",
    "#  lines(true_model,col=\"green\")\n",
    "# cov.prob, analytical standard errors\n",
    "paste('Coverage Probability, analytical standard errors:     ', mean(result_1))\n",
    "# cov_ probability, \n",
    "paste('Coverage Probability:                                                  ',mean(result_1B))\n",
    "# interval length ratio sum, if >0.5*N: \n",
    "paste('Interval length ratio sum, if >0.5*N:                           ',mean(result_2))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length:                                                     ',mean(result_int))\n",
    "# avg.interval_length\n",
    "paste('avg Interval length (B):                                               ',mean(result_int_B))"
   ]
  }
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