ESTIMATION AND VARIABLE SELECTION FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELS

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...

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Bibliographic Details
Published inThe Annals of statistics Vol. 39; no. 4; p. 1827
Main Authors Wang, Li, Liu, Xiang, Liang, Hua, Carroll, Raymond J
Format Journal Article
LanguageEnglish
Published United States 01.08.2011
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/11-aos885