node13.htm

来自「matlab bootstrap程序设计方法」· HTM 代码 · 共 111 行

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"><!--Converted with LaTeX2HTML 2002-2 (1.70)original version by:  Nikos Drakos, CBLU, University of Leeds* revised and updated by:  Marcus Hennecke, Ross Moore, Herb Swan* with significant contributions from:  Jens Lippmann, Marek Rouchal, Martin Wilck and others --><HTML><HEAD><TITLE>Balanced Bootstraps</TITLE><META NAME="description" CONTENT="Balanced Bootstraps"><META NAME="keywords" CONTENT="web1"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><META NAME="Generator" CONTENT="LaTeX2HTML v2002-2"><META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css"><LINK REL="STYLESHEET" HREF="web1.css"><LINK REL="next" HREF="node14.html"><LINK REL="previous" HREF="node12.html"><LINK REL="up" HREF="node6.html"><LINK REL="next" HREF="node14.html"></HEAD><BODY ><!--Navigation Panel--><A NAME="tex2html332"  HREF="node14.html"><IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="file:/home/depot/swtree/depot/latex2html-2002-2/latex2html-2002-2/icons/next.png"></A> <A NAME="tex2html330"  HREF="node6.html"><IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="file:/home/depot/swtree/depot/latex2html-2002-2/latex2html-2002-2/icons/up.png"></A> <A NAME="tex2html324"  HREF="node12.html"><IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="file:/home/depot/swtree/depot/latex2html-2002-2/latex2html-2002-2/icons/prev.png"></A>   <BR><B> Next:</B> <A NAME="tex2html333"  HREF="node14.html">Monte Carlo</A><B> Up:</B> <A NAME="tex2html331"  HREF="node6.html">Lectures</A><B> Previous:</B> <A NAME="tex2html325"  HREF="node12.html">Complete Enumeration</A><BR><BR><!--End of Navigation Panel--><H1><A NAME="SECTION00270000000000000000">Balanced Bootstraps</A></H1><BODY bgcolor="#FFFFFF"><P>Intermediary between the complete enumerationof all samples and the drawing of a few samplesat random lies the Balanced Bootstrap,(see Gleason, 1988, American Statistician,263-266)for a simple algorithm.<P>The idea is that as when we count all <IMG WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="img150.png" ALT="$\vert C_n\vert$"> sampleseach observation has the same chance of appearing,we would like to have each observation appearingoverall the same number of times after all <IMG WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img32.png" ALT="$B$"> bootstrap resamples have been drawn.<P>We can be ensured of this by taking a list of <IMG WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img32.png" ALT="$B$">repetitions of each of the observations<!-- MATH $x_1,x_2,\ldots, x_n$ --><IMG WIDTH="111" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" SRC="img151.png" ALT="$x_1,x_2,\ldots, x_n$"> and repeating them <IMG WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img32.png" ALT="$B$"> times,take a permutation of these <IMG WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img152.png" ALT="$nB$"> values and then take the first <IMG WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img28.png" ALT="$n$"> asthe first sample, and so on.<P><BR><HR><ADDRESS>Susan Holmes2004-05-19</ADDRESS></BODY></HTML>

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