The Variable Selection Problem In Cox Model And Cox Model With Varying Coefficients Based On The Adaptive LASSO Method

The variable selection problem in Cox model and Cox model with varying coefficients is considered. It’s based on penalizing partial likelihood function with Adaptive LASSO. Second order Taylor Formula and B-splines are used re spectively to expand the function. To solve the model, this paper applies Cycli cal Coordinate Descent algorithm to complete the whole variable selection and Estimation procedure. As for the selection of the Adjustment parameters, 10-Fo ld Cross Validation and Generalized Cross Validation are used in this paper. In the case of Cox model, the result of the simulation shows that with the help of CCD algorithm, the Adaptive LASSO performs better than traditional variabl e selection method and LASSO, also, the computing speed and the efficiency i s greatly improved. In the case of Cox model with varying coefficients, the eff iciency of the variable selection is influenced by three factors: the type of vari ables, the censored rate and the scale effect. As for the types of the variable s:Irrelevant variables> fixed –coefficient variables> completely dependent varia bles> Semi-dependent variables. Also for the last two factors, the lower the ce nsored rate, the better the variable selection efficiency and the smaller the scal e effect, the greater the possibility of being selected for the Semi-dependent va riables. What’s more, this method can also distinguish between fixed-coefficient variables and varying-coefficient variables. Finally, this method will be used t o select and estimate the important financial factors of listed companies by con structing financial crisis model with Cox model and Cox model of varying coe fficients.