ON THE CONSISTENCY OF THE M << N BOOTSTRAP APPROXIMATION FOR A TRIMMED MEAN

被引：5
|
作者：
Gribkova, N. V. [1 ]
Helmers, R. [2 ]
机构：
[1] St Petersburg State Univ, Math & Mech Fac, St Petersburg 198504, Stary Peterhof, Russia
[2] Ctr Math & Comp Sci, NL-1090 GB Amsterdam, Netherlands
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2011年 / 55卷 / 01期
关键词：
M out of N bootstrap; trimmed mean; asymptotic normality; consistency of the M << N bootstrap approximation; modified bootstrap; ASYMPTOTIC-DISTRIBUTION;
D O I：
10.1137/S0040585X97984607
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We show that the M << N (N is the original data sample size, M denotes the size of the bootstrap resample; M/N -> 0, as M -> infinity) bootstrap approximation of the distribution of the trimmed mean is consistent without any conditions upon the population distribution F, whereas Efron's naive (i.e., M = N) bootstrap, as well as the normal approximation, fails to be consistent if the population distribution F has gaps at those two quantiles where the trimming occurs.
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页码：42 / 53
页数：12
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