# The Weighted Bootstrap

• Philippe Barbe
• Patrice Bertail
Book

Part of the Lecture Notes in Statistics book series (LNS, volume 98)

1. Front Matter
Pages ii-x
2. Philippe Barbe, Patrice Bertail
Pages 1-8
3. Philippe Barbe, Patrice Bertail
Pages 9-43
4. Philippe Barbe, Patrice Bertail
Pages 45-76
5. Philippe Barbe, Patrice Bertail
Pages 77-91
6. Philippe Barbe, Patrice Bertail
Pages 93-118
7. Philippe Barbe, Patrice Bertail
Pages 119-144
8. Philippe Barbe, Patrice Bertail
Pages 145-152
9. Back Matter
Pages 153-233

### Introduction

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.

### Keywords

Bootstrapping Estimator Parameter Power Variance statistics

#### Authors and affiliations

• Philippe Barbe
• 1
• Patrice Bertail
• 2
1. 1.CNRS, Laboratoire de Statistiques et ProbabilitéUniversité Paul SabatierToulouse CedexFrance
2. 2.INRA-CORELAIvry sur Seine CedexFrance

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-2532-4
• Copyright Information Springer-Verlag New York 1995
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-94478-4
• Online ISBN 978-1-4612-2532-4
• Series Print ISSN 0930-0325
• Buy this book on publisher's site