The Weighted Bootstrap

von Philippe Barbe, Patrice Bertail

230 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Statistics
• Themen: Mathematik und Naturwissenschaften Mathematik Wahrscheinlichkeitsrechnung und Statistik
• ISBN: 9780387944784
• Sprache: Englisch
• Erscheinungsdatum: 24.02.1995
• Größe: 23.5 x 15.5 cm
• Verlag: Springer US