Estimation and variable selection for generalized additive partial linear models

Handle URI:
http://hdl.handle.net/10754/598236
Title:
Estimation and variable selection for generalized additive partial linear models
Authors:
Wang, Li; Liu, Xiang; Liang, Hua; Carroll, Raymond J.
Abstract:
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.
Citation:
Wang L, Liu X, Liang H, Carroll RJ (2011) Estimation and variable selection for generalized additive partial linear models. The Annals of Statistics 39: 1827–1851. Available: http://dx.doi.org/10.1214/11-AOS885.
Publisher:
Institute of Mathematical Statistics
Journal:
The Annals of Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Aug-2011
DOI:
10.1214/11-AOS885
Type:
Article
ISSN:
0090-5364
Sponsors:
Supported by NSF Grant DMS-09-05730.Supported by a Merck Quantitative Sciences Fellowship Program.Supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWang, Lien
dc.contributor.authorLiu, Xiangen
dc.contributor.authorLiang, Huaen
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-25T13:17:08Zen
dc.date.available2016-02-25T13:17:08Zen
dc.date.issued2011-08en
dc.identifier.citationWang L, Liu X, Liang H, Carroll RJ (2011) Estimation and variable selection for generalized additive partial linear models. The Annals of Statistics 39: 1827–1851. Available: http://dx.doi.org/10.1214/11-AOS885.en
dc.identifier.issn0090-5364en
dc.identifier.doi10.1214/11-AOS885en
dc.identifier.urihttp://hdl.handle.net/10754/598236en
dc.description.abstractWe study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.en
dc.description.sponsorshipSupported by NSF Grant DMS-09-05730.Supported by a Merck Quantitative Sciences Fellowship Program.Supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectBackfittingen
dc.subjectGeneralized additive modelsen
dc.subjectGeneralized partially linear modelsen
dc.subjectLASSOen
dc.subjectNonconcave penalized likelihooden
dc.subjectPenalty-based variable selectionen
dc.subjectPolynomial splineen
dc.subjectQuasi-likelihooden
dc.subjectSCADen
dc.subjectShrinkage methods.en
dc.titleEstimation and variable selection for generalized additive partial linear modelsen
dc.typeArticleen
dc.identifier.journalThe Annals of Statisticsen
dc.contributor.institutionThe University of Georgia, Athens, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionUniversity of Rochester, Rochester, United Statesen
kaust.grant.numberKUS-CI-016-04en
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