Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data

Handle URI:
http://hdl.handle.net/10754/598118
Title:
Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data
Authors:
Carroll, Raymond; Maity, Arnab; Mammen, Enno; Yu, Kyusang
Abstract:
We consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.
Citation:
Carroll R, Maity A, Mammen E, Yu K (2009) Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data. Stat Biosci 1: 10–31. Available: http://dx.doi.org/10.1007/s12561-009-9000-7.
Publisher:
Springer Nature
Journal:
Statistics in Biosciences
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
23-Apr-2009
DOI:
10.1007/s12561-009-9000-7
PubMed ID:
20161464
PubMed Central ID:
PMC2791377
Type:
Article
ISSN:
1867-1764; 1867-1772
Sponsors:
Yu and Mammen’s research was supported by the Deutsche Forschungsgemein-schaft project MA 1026/7-3. Carroll and Maity’s research was supported by a grant from the NationalCancer Institute (CA57030). Carroll’s work was also supported by Award Number KUS-CI-016-04, madeby King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorCarroll, Raymonden
dc.contributor.authorMaity, Arnaben
dc.contributor.authorMammen, Ennoen
dc.contributor.authorYu, Kyusangen
dc.date.accessioned2016-02-25T13:13:01Zen
dc.date.available2016-02-25T13:13:01Zen
dc.date.issued2009-04-23en
dc.identifier.citationCarroll R, Maity A, Mammen E, Yu K (2009) Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data. Stat Biosci 1: 10–31. Available: http://dx.doi.org/10.1007/s12561-009-9000-7.en
dc.identifier.issn1867-1764en
dc.identifier.issn1867-1772en
dc.identifier.pmid20161464en
dc.identifier.doi10.1007/s12561-009-9000-7en
dc.identifier.urihttp://hdl.handle.net/10754/598118en
dc.description.abstractWe consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.en
dc.description.sponsorshipYu and Mammen’s research was supported by the Deutsche Forschungsgemein-schaft project MA 1026/7-3. Carroll and Maity’s research was supported by a grant from the NationalCancer Institute (CA57030). Carroll’s work was also supported by Award Number KUS-CI-016-04, madeby King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.titleEfficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Dataen
dc.typeArticleen
dc.identifier.journalStatistics in Biosciencesen
dc.identifier.pmcidPMC2791377en
dc.contributor.institutionDepartment of Statistics, 3143 TAMU, Texas A&M University, College Station, Texas 77843, USA, carroll@stat.tamu.edu , Telephone 979 845 3141, Fax 979 845 3144.en
kaust.grant.numberKUS-CI-016-04en

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