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Journal of Applied Mathematics
Volume 2014, Article ID 360249, 16 pages
Research Article

New Inference Procedures for Semiparametric Varying-Coefficient Partially Linear Cox Models

1School of Statistics and Research Center of Statistics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2Information Engineering University, Zhengzhou, Henan 450001, China

Received 14 October 2013; Accepted 19 March 2014; Published 25 May 2014

Academic Editor: Jinyun Yuan

Copyright © 2014 Yunbei Ma and Xuan Luo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.