Variable Selection for Partially Linear Models with Randomly Censored Data

Abstract

Abstract This article proposes a variable selection procedure for partially linear models with right-censored data via penalized least squares. We apply the SCAD penalty to select significant variables and estimate unknown parameters simultaneously. The sampling properties for the proposed procedure are investigated. The rate of convergence and the asymptotic normality of the proposed estimators are established. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property. In addition, an iterative algorithm is proposed to find the solution of the penalized least squares. Simulation studies are conducted to examine the finite sample performance of the proposed method. Keywords: Censored dataOracle propertyPartially linear modelsSCADVariable selectionMathematics Subject Classification: 62G0562G20 Acknowledgments This research was supported by the National Natural Science Foundation of China (Grant No. 10871013), the National Natural Science Foundation of Beijing (Grant No. 1102008, 1062001), and Ph.D. program Foundation of Ministry of Education of China (20070005003) and PHR(IHLB).