cap1/MADsmallsample.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# <span style=\"color:rgb(213,80,0)\">Analysis of consistency factor (small sample and asymptotic for MAD).</span>\n",
    "\n",
    "This file creates Figure 1.1\n",
    "\n",
    "## Empirical consisteny factor for MAD when n=5\n",
    "\n",
    "Take n observations from N(0,1) and compute the MAD Repeat the experiment nsimul times and compute the average of the MADs\n",
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "source": [
    "nsimul=1000000;\n",
    "n=5;\n",
    "MAD=zeros(nsimul,1);\n",
    "for j=1:nsimul\n",
    "    x=randn(n,1);\n",
    "    MAD(j)=mad(x,1);\n",
    "end\n",
    "Mea=mean(MAD);\n",
    "disp(Mea)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          0.55"
      ]
     },
     "metadata": {},
     "execution_count":  1,
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare the input data for Figure 1.1\n",
    "\n",
    "Repeat the previous simulation study for each value of nn=5, 6, ..., 100\n",
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "source": [
    "nsimul=10000; % Use nsimul=1000000 for greater precision\n",
    "nn=5:100;\n",
    "maxnn=nn(end);\n",
    "minnn=nn(1);\n",
    "MADall=NaN(maxnn-minnn+1,1);\n",
    "\n",
    "for i=nn\n",
    "    MAD=zeros(nsimul,1);\n",
    "\n",
    "    parfor j=1:nsimul\n",
    "        MAD(j)=mad(randn(i,1),1);\n",
    "    end\n",
    "    Mea=mean(MAD);\n",
    "    MADall(i-minnn+1)=Mea;\n",
    "    disp(['sample size n=' num2str(i)])\n",
    "end"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sample size n=5\n",
       "sample size n=6\n",
       "sample size n=7\n",
       "sample size n=8\n",
       "sample size n=9\n",
       "sample size n=10\n",
       "sample size n=11\n",
       "sample size n=12\n",
       "sample size n=13\n",
       "sample size n=14\n",
       "sample size n=15\n",
       "sample size n=16\n",
       "sample size n=17\n",
       "sample size n=18\n",
       "sample size n=19\n",
       "sample size n=20\n",
       "sample size n=21\n",
       "sample size n=22\n",
       "sample size n=23\n",
       "sample size n=24\n",
       "sample size n=25\n",
       "sample size n=26\n",
       "sample size n=27\n",
       "sample size n=28\n",
       "sample size n=29\n",
       "sample size n=30\n",
       "sample size n=31\n",
       "sample size n=32\n",
       "sample size n=33\n",
       "sample size n=34\n",
       "sample size n=35\n",
       "sample size n=36\n",
       "sample size n=37\n",
       "sample size n=38\n",
       "sample size n=39\n",
       "sample size n=40\n",
       "sample size n=41\n",
       "sample size n=42\n",
       "sample size n=43\n",
       "sample size n=44\n",
       "sample size n=45\n",
       "sample size n=46\n",
       "sample size n=47\n",
       "sample size n=48\n",
       "sample size n=49\n",
       "sample size n=50\n",
       "sample size n=51\n",
       "sample size n=52\n",
       "sample size n=53\n",
       "sample size n=54\n",
       "sample size n=55\n",
       "sample size n=56\n",
       "sample size n=57\n",
       "sample size n=58\n",
       "sample size n=59\n",
       "sample size n=60\n",
       "sample size n=61\n",
       "sample size n=62\n",
       "sample size n=63\n",
       "sample size n=64\n",
       "sample size n=65\n",
       "sample size n=66\n",
       "sample size n=67\n",
       "sample size n=68\n",
       "sample size n=69\n",
       "sample size n=70\n",
       "sample size n=71\n",
       "sample size n=72\n",
       "sample size n=73\n",
       "sample size n=74\n",
       "sample size n=75\n",
       "sample size n=76\n",
       "sample size n=77\n",
       "sample size n=78\n",
       "sample size n=79\n",
       "sample size n=80\n",
       "sample size n=81\n",
       "sample size n=82\n",
       "sample size n=83\n",
       "sample size n=84\n",
       "sample size n=85\n",
       "sample size n=86\n",
       "sample size n=87\n",
       "sample size n=88\n",
       "sample size n=89\n",
       "sample size n=90\n",
       "sample size n=91\n",
       "sample size n=92\n",
       "sample size n=93\n",
       "sample size n=94\n",
       "sample size n=95\n",
       "sample size n=96\n",
       "sample size n=97\n",
       "sample size n=98\n",
       "sample size n=99\n",
       "sample size n=100"
      ]
     },
     "metadata": {},
     "execution_count":  2,
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "source": [
    "\n",
    "disp('Empirical consistenty factor when n=100')"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Empirical consistenty factor when n=100"
      ]
     },
     "metadata": {},
     "execution_count":  3,
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "source": [
    "disp(1./MADall(end))"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.49"
      ]
     },
     "metadata": {},
     "execution_count":  4,
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "source": [
    "% Using nsimul=100,000,000 when n=100\n",
    "% the empirical consistency factor is 1.4942"
   ],
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "source": [
    "close all\n",
    "plot(nn,1./MADall)\n",
    "xlabel('Sample size')\n",
    "yline(1/norminv(0.75))\n",
    "xlim([minnn maxnn])\n",
    "ylabel('Empirical consistency factor')\n",
    "\n",
    "prin=0;\n",
    "if prin==1\n",
    "    % print to postscript\n",
    "    print -depsc simMAD.eps;\n",
    "else\n",
    "    title('Figure 1.1')\n",
    "    set(gcf,'Name','Figure 1.1')\n",
    "\n",
    "end"
   ],
   "outputs": [
    {
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width=\"562\" alt=\"figure_0.png\"></center>"
      ]
     },
     "metadata": {},
     "execution_count":  6,
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "source": [
    "\n",
    "%InsideREADME"
   ],
   "outputs": []
}
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "MATLAB (matlabkernel)",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "file_extension": ".m",
   "mimetype": "text/matlab",
   "name": "matlab",
   "nbconvert_exporter": "matlab",
   "pygments_lexer": "matlab",
   "version": "25.1.0.2802752"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}