General Weak Laws of Large Numbers for Bootstrap Sample Means

Authors: John H. J. Einmahl ^a; Andrew Rosalsky ^b

Affiliations:	^a Department of Econometrics and OR, Tilburg University, Tilburg, The Netherlands
	^b Department of Statistics, University of Florida, Gainesville, Florida, USA

DOI: 10.1081/SAP-200064490

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 23, Issue 4 July 2005 , pages 853 - 869

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: HTML (English) : PDF (English)

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Abstract

For bootstrap sample means resulting from a sequence lcub

X_n, n ≥ 1 rcub

of random variables, very general weak laws of large numbers are established. The random variables lcub

X_n, n ≥ 1 rcub

do not need to be independent or identically distributed or be of any particular dependence structure. In general, no moment conditions are imposed on the lcub

X_n, n ≥ 1 rcub

. Examples are provided that illustrate the sharpness of the main results.

Keywords: Almost sure convergence; Bootstrap sample mean; Convergence in probability; Weak law of large numbers

Mathematics Subject Classification: Primary 60F05, 62G09; Secondary 62G20

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General Weak Laws of Large Numbers for Bootstrap Sample Means

Abstract