Estimation and variable selection for generalized additive partial linear models

Li Wang, Xiang Liu, Hua Liang, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review

91 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1827-1851
Number of pages25
JournalThe Annals of Statistics
Volume39
Issue number4
DOIs
StatePublished - Aug 2011
Externally publishedYes

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