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.

引用

页码：42 / 53

页数：12

共 50 条

[41] A Note on Asymptotic Distribution of Trimmed Mean
Dhar, Subhra Sankar
Chatterjee, Udita
Shalabh
JOURNAL OF THE INDIAN SOCIETY FOR PROBABILITY AND STATISTICS, 2022, 23 (02) : 327 - 335
[42] ADAPTIVE TRIMMED MEAN AS A LOCATION ESTIMATE
Siming LI
Yong LI
Jiao JIN
JournalofSystemsScience&Complexity, 2012, 25 (05) : 973 - 986
[43] Adaptive trimmed mean as a location estimate
Siming Li
Yong Li
Jiao Jin
Journal of Systems Science and Complexity, 2012, 25 : 973 - 986
[44] High breakdown analogs of the trimmed mean
Olive, DJ
STATISTICS & PROBABILITY LETTERS, 2001, 51 (01) : 87 - 92
[45] A Note on Asymptotic Distribution of Trimmed Mean
Subhra Sankar Dhar
Udita Chatterjee
Journal of the Indian Society for Probability and Statistics, 2022, 23 : 327 - 335
[46] On the choice of m in the m out of n bootstrap and confidence bounds for extrema
Bickel, Peter J.
Sakov, Anat
STATISTICA SINICA, 2008, 18 (03) : 967 - 985
[47] On a class of m out of n bootstrap confidence intervals
Lee, SMS
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 1999, 61 : 901 - 911
[48] SOME STATISTICAL PROPERTIES OF ALPHA-TRIMMED MEAN AND STANDARD TYPE-M FILTERS
PETERSON, SR
LEE, YH
KASSAM, SA
IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1988, 36 (05): : 707 - 713
[49] THE BOOTSTRAP OF THE MEAN WITH ARBITRARY BOOTSTRAP SAMPLE-SIZE
ARCONES, MA
GINE, E
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 1989, 25 (04): : 457 - 481
[50] Consistency of the Subsample Bootstrap empirical process
Pauly, Markus
STATISTICS, 2012, 46 (05) : 621 - 626

← 1 2 3 4 5 →