Bootstrapping the sample means for stationary mixing sequences
type: Item
instance of: scholarly article
title: Bootstrapping the sample means for stationary mixing sequences
zbMATH Open document ID: 0802.62048
DOI: 10.1016/0304-4149(93)90113-I
author: Hao Yu
author: Q. M. Shao
published in: Stochastic Processes and their Applications
publication date: 1994-12-07T00:00:00Z
review text: To make the bootstrap suitable for dependent observations many authors [among them \textit{H. R. Künsch}, Ann. Stat. 17, No. 3, 1217-1241 (1989; Zbl 0684.62035)] have introduced various block resampling procedures. In this paper a circular block resampling procedure, modifying Künsch's procedure, is proposed. This procedure has the special feature that the resampled data are like drawing from the empirical distribution function of dependent observations. No information is lost concerning the nature of dependency of the original observations coming from a general stationary sequence. Two general theorems on bootstrapping sample means for stationary sequences are proved. Applications to stationary \(\alpha\)-mixing, \(\rho\)- mixing and \(\varphi\)-mixing sequences are also discussed.
Mathematics Subject Classification ID: 62G09
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 488403
zbMATH Keywords: alpha-mixing
zbMATH Keywords: rho-mixing
zbMATH Keywords: phi-mixing
zbMATH Keywords: bootstrap
zbMATH Keywords: dependent observations
zbMATH Keywords: circular block resampling procedure
zbMATH Keywords: empirical distribution
zbMATH Keywords: dependency
zbMATH Keywords: general stationary sequence
zbMATH Keywords: bootstrapping sample means
reviewed by: Jarosław Bartoszewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 488403