Estimation and variable selection for generalized additive partial linear models

TL;DR

This paper introduces a computationally efficient method for estimating and selecting variables in generalized additive partial linear models using polynomial spline smoothing and penalized quasi-likelihood, with proven asymptotic properties.

Contribution

It develops a novel estimation approach with variable selection for these models, achieving asymptotic normality and oracle properties.

Findings

Estimation method is computationally simpler than kernel-based approaches.

Variable selection procedure has oracle property.

Simulation and empirical results demonstrate effectiveness.

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.