A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem

Handle URI:
http://hdl.handle.net/10754/597252
Title:
A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem
Authors:
Delaigle, Aurore; Fan, Jianqing; Carroll, Raymond J.
Abstract:
Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.
Citation:
Delaigle A, Fan J, Carroll RJ (2009) A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem. Journal of the American Statistical Association 104: 348–359. Available: http://dx.doi.org/10.1198/jasa.2009.0114.
Publisher:
Informa UK Limited
Journal:
Journal of the American Statistical Association
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Mar-2009
DOI:
10.1198/jasa.2009.0114
PubMed ID:
20351800
PubMed Central ID:
PMC2846380
Type:
Article
ISSN:
0162-1459; 1537-274X
Sponsors:
Carroll's research was supported by grants from the National Cancer Institute (CA57030, CA90301) and by award number KUS-CI-016-04 made by the King Abdullah University of Science and Technology (KAUST). Delaigle's research was supported by a Maurice Belz Fellowship from the University of Melbourne, Australia, and by a grant from the Australian Research Council. Fan's research was supported by grants from the National Institute of General Medicine R01-GM072611 and National Science Foundation DMS-0714554 and DMS-0751568. The authors thank the editor, the associate editor, and referees for their valuable comments.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDelaigle, Auroreen
dc.contributor.authorFan, Jianqingen
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-25T12:29:00Zen
dc.date.available2016-02-25T12:29:00Zen
dc.date.issued2009-03en
dc.identifier.citationDelaigle A, Fan J, Carroll RJ (2009) A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem. Journal of the American Statistical Association 104: 348–359. Available: http://dx.doi.org/10.1198/jasa.2009.0114.en
dc.identifier.issn0162-1459en
dc.identifier.issn1537-274Xen
dc.identifier.pmid20351800en
dc.identifier.doi10.1198/jasa.2009.0114en
dc.identifier.urihttp://hdl.handle.net/10754/597252en
dc.description.abstractLocal polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.en
dc.description.sponsorshipCarroll's research was supported by grants from the National Cancer Institute (CA57030, CA90301) and by award number KUS-CI-016-04 made by the King Abdullah University of Science and Technology (KAUST). Delaigle's research was supported by a Maurice Belz Fellowship from the University of Melbourne, Australia, and by a grant from the Australian Research Council. Fan's research was supported by grants from the National Institute of General Medicine R01-GM072611 and National Science Foundation DMS-0714554 and DMS-0751568. The authors thank the editor, the associate editor, and referees for their valuable comments.en
dc.publisherInforma UK Limiteden
dc.subjectBandwidth selectoren
dc.subjectDeconvolutionen
dc.subjectInverse problemsen
dc.subjectLocal polynomialen
dc.subjectMeasurement errorsen
dc.subjectNonparametric regressionen
dc.subjectReplicated measurementsen
dc.titleA Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problemen
dc.typeArticleen
dc.identifier.journalJournal of the American Statistical Associationen
dc.identifier.pmcidPMC2846380en
dc.contributor.institutionAurore Delaigle is Reader, Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK and Department of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia (E-mail: aurore.delaigle@bri-s.ac.uk ).en
kaust.grant.numberKUS-CI-016-04en

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