Nonparametric censored regression by smoothing splines
This thesis focuses on nonparametric regression for censored data via smoothing splines. The estimation of the mean function of survival time is considered, when the effect of the covariates is connected with a transformation of the response. An estimation procedure which uses smoothing splines is proposed. It is shown that the smoothing spline estimator is comparable to and complementary with the local linear estimator studied by Fan and Gijbels (1994). The proposed procedure has the advantage of using standard statistical packages, such as SAS, without much additional programming. The asymptotic normality for the smoothing spline estimator for the univariate case, with Leurgans' (1987) transformation of the response to account for censoring, is established by using counting processes and martingale techniques.