Bootstrap consistency for general semiparametric M-estimation

Handle URI:
http://hdl.handle.net/10754/597690
Title:
Bootstrap consistency for general semiparametric M-estimation
Authors:
Cheng, Guang; Huang, Jianhua Z.
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.
Citation:
Cheng G, Huang JZ (2010) Bootstrap consistency for general semiparametric M-estimation. The Annals of Statistics 38: 2884–2915. Available: http://dx.doi.org/10.1214/10-AOS809.
Publisher:
Institute of Mathematical Statistics
Journal:
The Annals of Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Oct-2010
DOI:
10.1214/10-AOS809
Type:
Article
ISSN:
0090-5364
Sponsors:
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).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCheng, Guangen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T12:44:28Zen
dc.date.available2016-02-25T12:44:28Zen
dc.date.issued2010-10en
dc.identifier.citationCheng G, Huang JZ (2010) Bootstrap consistency for general semiparametric M-estimation. The Annals of Statistics 38: 2884–2915. Available: http://dx.doi.org/10.1214/10-AOS809.en
dc.identifier.issn0090-5364en
dc.identifier.doi10.1214/10-AOS809en
dc.identifier.urihttp://hdl.handle.net/10754/597690en
dc.description.abstractConsider 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.en
dc.description.sponsorshipSupported 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).en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectBootstrap confidence seten
dc.subjectBootstrap consistencyen
dc.subjectM-estimationen
dc.subjectSemiparametric modelen
dc.titleBootstrap consistency for general semiparametric M-estimationen
dc.typeArticleen
dc.identifier.journalThe Annals of Statisticsen
dc.contributor.institutionPurdue University, West Lafayette, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-CI-016-04en
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