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Estimation and variable selection for generalized additive partial linear models. (English) Zbl 1227.62053
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.

62J12 Generalized linear models (logistic models)
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
65D10 Numerical smoothing, curve fitting
65C05 Monte Carlo methods
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