Overview
- Authors:
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Philippe Barbe
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CNRS, Laboratoire de Statistiques et Probabilité, Université Paul Sabatier, Toulouse Cedex, France
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Patrice Bertail
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INRA-CORELA, Ivry sur Seine Cedex, France
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Table of contents (7 chapters)
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- Philippe Barbe, Patrice Bertail
Pages 1-8
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- Philippe Barbe, Patrice Bertail
Pages 9-43
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- Philippe Barbe, Patrice Bertail
Pages 45-76
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- Philippe Barbe, Patrice Bertail
Pages 77-91
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- Philippe Barbe, Patrice Bertail
Pages 93-118
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- Philippe Barbe, Patrice Bertail
Pages 119-144
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- Philippe Barbe, Patrice Bertail
Pages 145-152
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Back Matter
Pages 153-233
About this book
INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.
Authors and Affiliations
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CNRS, Laboratoire de Statistiques et Probabilité, Université Paul Sabatier, Toulouse Cedex, France
Philippe Barbe
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INRA-CORELA, Ivry sur Seine Cedex, France
Patrice Bertail
