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August 2010 Penalized variable selection procedure for Cox models with semiparametric relative risk
Pang Du, Shuangge Ma, Hua Liang
Ann. Statist. 38(4): 2092-2117 (August 2010). DOI: 10.1214/09-AOS780

Abstract

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate effect function, provides a smoothing spline ANOVA framework that is exploited to derive an empirical model selection tool for the nonparametric part. The second penalty, either the smoothly-clipped-absolute-deviation (SCAD) penalty or the adaptive LASSO penalty, achieves variable selection in the parametric part. We show that the resulting estimator of the parametric part possesses the oracle property, and that the estimator of the nonparametric part achieves the optimal rate of convergence. The proposed procedures are shown to work well in simulation experiments, and then applied to a real data example on sexually transmitted diseases.

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Pang Du. Shuangge Ma. Hua Liang. "Penalized variable selection procedure for Cox models with semiparametric relative risk." Ann. Statist. 38 (4) 2092 - 2117, August 2010. https://doi.org/10.1214/09-AOS780

Information

Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1202.62132
MathSciNet: MR2676884
Digital Object Identifier: 10.1214/09-AOS780

Subjects:
Primary: 62N01 , 62N03
Secondary: 62N02

Keywords: backfitting , partially linear models , penalized partial likelihood , penalized variable selection , proportional hazards , Smoothing spline ANOVA

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 4 • August 2010
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