Bootstraps of sums of independent but not identically distributed stochastic processes
type: Item
instance of: scholarly article
title: Bootstraps of sums of independent but not identically distributed stochastic processes
zbMATH Open document ID: 1016.62063
DOI: 10.1016/S0047-259X(02)00040-4
author: Michael R. Kosorok
published in: Journal of Multivariate Analysis
publication date: 2003-05-19T00:00:00Z
review text: A central limit theorem for sums of independent, but not identically distributed stochastic processes multiplied by independent real random variables with mean zero is developed. Weak convergence of the Hoffmann-Jorgensen-Dudley type, as described by \textit{A. van der Vaart} and \textit{J. A. Wellner} [Weak convergence and empirical processes. With applications to statistics. (1996; Zbl 0862.60002)], is utilized. These results allow Monte Carlo estimation of limiting probability measures obtained from application of \textit{D. Pollard} 's [Empirical processes: theory and applications. (1990; Zbl 0741.60001)] functional central limit theorem for empirical processes. An application of this theory to the two-parameter Cox score process with staggered entry data is given for illustration. For this process, the proposed multiplier bootstrap appears to be the first successful method for estimating the associated limiting distribution. The results of this paper complement previous bootstrap and multiplier central limit theorems for i.i.d. empirical processes. The references contain 17 bibliographical hints.
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 62G99
Mathematics Subject Classification ID: 62G09
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1912390
zbMATH Keywords: Functional central limit theorem
zbMATH Keywords: General empirical process
zbMATH Keywords: Hoffmann-Jorgensen-Dudley weak convergence
zbMATH Keywords: Manageability
zbMATH Keywords: Two-parameter
zbMATH Keywords: Cox score process
MaRDI profile type: Publication
cites work: Central limit theorems for stochastic processes under random entropy conditions
cites work: The central limit theorem and the law of iterated logarithm for empirical processes under local conditions
cites work: Towards a general asymptotic theory for Cox model with staggered entry
cites work: Supremum Versions of the Log-Rank and Generalized Wilcoxon Statistics
cites work: Empirical processes indexed by Lipschitz functions
cites work: Weak convergence of time-sequential censored rank statistics with applications to sequential testing in clinical trials
cites work: Un critère sur les petites boules dans le théorème limite central. (A criterion on small balls in the central limit theorem)
cites work: Accelerated failure time models for counting processes
cites work: A rank statistics approach to the consistency of a general bootstrap
cites work: Q4001821
cites work: Q4315057
cites work: Exchangeably weighted bootstraps of the general empirical process
cites work: Sequential analysis of the proportional hazards model
cites work: Sequential linear rank tests for two-sample censored survival data
cites work: Weak convergence and empirical processes. With applications to statistics
cites work: The adaptive biased coin design for sequential experiments
cites work: Functional central limit theorems for triangular arrays of function-indexed processes under uniformly integrable entropy conditions
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description: scientific article; zbMATH DE number 1912390