Estimation and variable selection for generalized additive partial linear models

Details Estimation and variable selection for generalized additive partial linear models Estimation and variable selection for generalized additive partial linear models

2011-12-12

arxiv.org/abs/1112.2502v1

Annals of Statistics 2011, Vol. 39, No. 4, 1827-1851

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS885 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS885

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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