Penalized Empirical Likelihood via Bridge Estimator in Cox's Proportional Hazard Model

Abstract

We propose the penalized empirical likelihood method via bridge estimator in Cox's proportional hazard model for parameter estimation and variable selection. Under reasonable conditions, we show that penalized empirical likelihood in Cox's proportional hazard model has oracle property. A penalized empirical likelihood ratio for the vector of regression coefficients is defined and its limiting distribution is a chi-square distributions. The advantage of penalized empirical likelihood as a nonparametric likelihood approach is illustrated in testing hypothesis and constructing confidence sets. The method is illustrated by extensive simulation studies and a real example.

Keywords:

• Bridge estimator
• Cox's proportional hazard model
• Empirical likelihood
• Variable selection

Mathematics Subject Classification:

• 62G05
• 62N01

Acknowledgments

The authors are grateful to the anonymous referees for the comments and suggestions which led to an improved presentation of the article.