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arXiv · 1112.2502

Estimation and variable selection for generalized additive partial linear models

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

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Li Wang, Xiang Liu, Hua Liang, Raymond J. Carroll. 2011-12-12. Estimation and variable selection for generalized additive partial linear models. https://doi.org/10.1214/11-aos885

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