Variable Selection In Partly Linear Regression Model For Right Censored Data

In this thesis, Based on Stute’s weighted least squares method, we consider the issue of the estimate procedures in partly linear regression model for right censored data whose covariate effects have two parts. The first part is for the low dimensional covariates and takes a nonparametric form, and the second part is for the high dimensional covariates and takes a parametric form. The selection of parametric covariate effects is achieved using a minimax concave penalty (MCP) approach. We point out that under the condition that the censoring rate is too high, the estimation consistency of the MCP in the semi-parameter accelerated failure time (AFT) model might not hold any more. We demonstrate that under the condition that the censoring rate is low, the MCP can select the true model consistently. The nonparametric component is estimated using a sieve approach. Furthermore, we define the likelihood function for the semi-parameter AFT model and establish the Bayes information criterion (BIC) for the AFT model. Numerical studies also show that our proposed approach has satisfactory performance.