Sequential Shrinkage Estimate for COX Regression Models with Uncertain Number of Effective Variables

In the applications of COX regression models, we always encounter data sets that contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “noneffective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model based on an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size. Fixed design is considered for numerical simulation. The strong consistency, asymptotic distributions and convergence rates of estimates under the fixed design are obtained. In addition, the sequential procedure is shown to be asymptotically optimal in the sense of Chow and Robbins (1965).