Bootstrap consistency for general semiparametric M-estimation

Guang Cheng, Jianhua Z. Huang

Research output: Contribution to journalArticlepeer-review

95 Scopus citations

Abstract

Consider M-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric M-estimation and, because of its simplicity, provides an attractive alternative to the inference approach based on the asymptotic distribution theory. The purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the M-estimate of Euclidean parameter; that is, the bootstrap distribution asymptotically imitates the distribution of the M-estimate. We also show that the bootstrap confidence set has the asymptotically correct coverage probability. These general onclusions hold, in particular, when the nuisance parameter is not estimable at root-n rate, and apply to a broad class of bootstrap methods with exchangeable ootstrap weights. This paper provides a first general theoretical study of the bootstrap in semiparametric models. © Institute of Mathematical Statistics, 2010.
Original languageEnglish (US)
Pages (from-to)2884-2915
Number of pages32
JournalThe Annals of Statistics
Volume38
Issue number5
DOIs
StatePublished - Oct 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Supported by NSF Grant DMS-09-06497.Supported in part by NSF Grants DMS-06-06580, DMS-09-07170, NCI Grant CA57030 and Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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