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SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

Acta Mathematicae Applicatae Sinica 2014年第4期30卷 887-902页

作者： Yue-Yong SHI Yong-Xiu CAO Yu-Ling JIAO Yan-Yan LIU School of Mathematics and Statistics Wuhan University

The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.

关键词： Cox proportional hazards models penalized partial likelihood diverging parameters oracle prop-erty smoothing quasi-newton

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Variable selection via generalized SELO-penalized linear regression models

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Applied Mathematics(A Journal of Chinese Universities) 2018年第2期33卷 145-162页

作者： SHI Yue-yong CAO Yong-xiu YU Ji-chang JIAO Yu-ling School of Econoraics and Management China University of GeosciencesWuhan 430074China School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China Center for Resources and Environmental Economic Research China University of GeosciencesWuhan 430074China

The seamless-L0 （SELO） penalty is a smooth function on [0, ∞） that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, we first generalize SELO to a class of penalties retaining good features of SELO, and then propose variable selection and estimation in linear models using the proposed generalized SELO （GSELO） penalized least squares （PLS） approach. We show that the GSELO-PLS procedure possesses the oracle property and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables. The entire path of GSELO-PLS estimates can be efficiently computed through a smoothing quasi-newton （SQN） method. A modified BIC coupled with a continuation strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.

关键词： continuation coordinate descent BIC LLA oracle property SELO smoothing quasi-newton

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