Abstract: Penalized empirical likelihood inferential procedure is proposed for Cox’s proportional hazards model with adaptive LASSO(ALASSO).Under reasonable conditions, we show that the proposed method has oracle property and the limiting distribution of a penalized empirical likelihood ratio via ALASSO is a chi-square distributions. The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets by simulation studies and a real example.

Key words: Cox’s proportional hazards model; , empirical likelihood; , ALASSO, variable selection