title: Sparse estimation of Cox proportional hazards models via approximated information criteria.
abstract: We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.
authors.affiliation: Department of Mathematical Sciences, University of Texas, El Paso, Texas, U.S.A.. xsu@utep.edu.
authors.forename: Xiaogang
authors.initials: X
authors.lastname: Su
authors.affiliation: Department of Mathematical Sciences, University of Texas, El Paso, Texas, U.S.A.
authors.forename: Chalani S
authors.initials: CS
authors.lastname: Wijayasinghe
authors.affiliation: Department of Mathematics and Statistics, San Diego State University, San Diego, California, U.S.A.
authors.forename: Juanjuan
authors.initials: J
authors.lastname: Fan
authors.affiliation: Department of Biostatistics, Indiana University Fairbanks School of Public Health and School of Medicine, Indianapolis, Indiana, U.S.A.|Department of Statistics, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Zhang
mesh_terms: D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D016016:Proportional Hazards Models
keywords: AIC; BIC; Cox proportional hazards model; Regularization; Sparse estimation; Variable selection