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GENERALIZED ADDITIVE PARTIAL LINEAR MODELS WITH HIGH-DIMENSIONAL COVARIATES

Published online by Cambridge University Press:  07 August 2013

Heng Lian  and
Hua Liang
Heng Lian
Affiliation:
Nanyang Technological University
Hua Liang
Affiliation:
University of Rochester
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Abstract

This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final selection and estimation results. We establish selection and estimation consistency of the estimator in addition to asymptotic normality for the estimator of the parametric components by employing a penalized quasi-likelihood. Thus our estimator is shown to have an asymptotic oracle property. Monte Carlo simulations show that the proposed procedure works well with moderate sample sizes.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 6 , December 2013 , pp. 1136 - 1161
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

1

We sincerely thank Professor Oliver Linton and two anonymous reviewers for their insightful and constructive comments, which have improved the manuscript significantly. Lian’s research was supported by Singapore MOE Tier 1 RG 62/11. Liang’s research was partially supported by NSF grants DMS-1007167 and DMS-1207444 and by Award 11228103 from the National Natural Science Foundation of China. Address correspondence to Hua Liang, Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA; e-mail: [email protected].

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