Semi-parametric Regression Model Consistency

This dissertation consists of two parts. We discuss semiparametric regression model and semiparametric regression model under random censorship respectively. The main purpose of the paper is to study their large sample properties.In part one, we consider semiparametric regression model under fixed design yi = xi + g(tl)+ i = 1, 2, ..., n, where 'is form an Lq-mixingale. We define the estimates n, gn for , g, and estibalish their consistency under suitable conditions using the least squares and the nearest neighbor estimator method.In part two, we deal with semiparametric regression model under random censorship yi* = xt + g(tt) + e i = 1, 2, ..., n, where e'is are independent, and Eet = 0. We define the estimates *n, g*n for , g, and estibalish their consistency under suitable conditions using the least squares and usual nonparametric weighted method.