Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

Handle URI:
http://hdl.handle.net/10754/598117
Title:
Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data
Authors:
Cheng, Guang; Zhou, Lan; Huang, Jianhua Z.
Abstract:
We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2014 ISI/BS.
Publisher:
Bernoulli Society for Mathematical Statistics and Probability
Journal:
Bernoulli
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Feb-2014
DOI:
10.3150/12-BEJ479
Type:
Article
ISSN:
1350-7265
Sponsors:
G. Cheng supported by NSF Grant DMS-09-06497 and NSF CAREER Award DMS-1151692. L. Zhou supported in part by NSF Grant DMS-09-07170. J. Z. Huang supported in part by NSF Grants DMS-06-06580, DMS-09-07170, NCI (CA57030), and 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.authorCheng, Guangen
dc.contributor.authorZhou, Lanen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T13:13:00Zen
dc.date.available2016-02-25T13:13:00Zen
dc.date.issued2014-02en
dc.identifier.issn1350-7265en
dc.identifier.doi10.3150/12-BEJ479en
dc.identifier.urihttp://hdl.handle.net/10754/598117en
dc.description.abstractWe consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2014 ISI/BS.en
dc.description.sponsorshipG. Cheng supported by NSF Grant DMS-09-06497 and NSF CAREER Award DMS-1151692. L. Zhou supported in part by NSF Grant DMS-09-07170. J. Z. Huang supported in part by NSF Grants DMS-06-06580, DMS-09-07170, NCI (CA57030), and Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherBernoulli Society for Mathematical Statistics and Probabilityen
dc.subjectGEEen
dc.subjectLink functionen
dc.subjectLongitudinal dataen
dc.subjectPartially linear additive modelsen
dc.subjectPolynomial splinesen
dc.titleEfficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered dataen
dc.typeArticleen
dc.identifier.journalBernoullien
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
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.