Open AccessESTIMATION AND VARIABLE SELECTION FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELS.
Author(s) -
Li Wang,
Xiang Liu,
Hua Liang,
Raymond J. Carroll
Publication year - 2011
Publication title -
pubmed
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.877
H-Index - 178
pISSN - 0090-5364
DOI - 10.1214/11-aos885supp
Subject(s) - mathematics , estimator , asymptotic distribution , empirical likelihood , model selection , mathematical optimization , linear model , spline (mechanical) , kernel smoother , estimating equations , smoothing spline , smoothing , kernel method , statistics , computer science , spline interpolation , structural engineering , artificial intelligence , radial basis function kernel , support vector machine , engineering , bilinear interpolation
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.