VARIABLE SELECTION IN PARTLY LINEAR REGRESSION MODEL WITH DIVERGING DIMENSIONS FOR RIGHT CENSORED DATA.

Recent biomedical studies often measure two distinct sets of risk factors: low-dimensional clinical and environmental measurements, and high-dimensional gene expression measurements. For prognosis studies with right censored response variables, we propose a semiparametric regression model whose covariate effects have two parts: a nonparametric part for low-dimensional covariates, and a parametric part for high-dimensional covariates. A penalized variable selection approach is developed. The selection of parametric covariate effects is achieved using an iterated Lasso approach, for which we prove the selection consistency property. The nonparametric component is estimated using a sieve approach. An empirical model selection tool for the nonparametric component is derived based on the Kullback-Leibler geometry. Numerical studies show that the proposed approach has satisfactory performance. Application to a lymphoma study illustrates the proposed method.