Shrinkage And Penalty Estimation In Gamma Censored Regression Models

This thesis mainly considers parameters estimation of Gamma censored regression model which has a wide range of applications in survival analysis field.Our purpose is applying stein-type shrinkage methods to improve performance of traditional estimation methods under the case where some predictor variables are uncorrelated to dependent variables. We discuss two models here, one is full model which considers all variables, the other is candidate model which deletes uncorrelated variables using priori information. It is found that estimator of combination of full model and candidate model shrinkage methods outperforms the estimator of which only one model is considered in terms of mean squared error. Furthermore,we also consider penalized estimator of Lasso, Adaptive Lasso and SCAD respectively and compare the performance of shrinkage methods and penalized methods.Simulation studies show that the shrinkage methods perform better than penalized methods. Two real data examples of oropharyngeal cancer and diabetes are given to demonstrate the usefulness of suggested method.