Some Research On Partially Linear Regression Models

In this article, the key studies are put on partially linear models with different set-tings. The main contents are as follows.(1)the studies of data transformation for linear regression. The method of estimation about the parameter λ in Box-Cox transformation and its extension are studied.(2) The semiparametric quantile re-gression model with a power transformation on the dependent variable is considered. The nonparametric part is estimated by the use of B-spline. The transformation pa-rameter is estimated by minimizing the cusum residual square sum. We obtain the uniformly rates of convergence about the estimations of semiparametric quantile regression.(3) The analysis of the partial linear regression model with censored data. Firstly, the censored data are substituted by K-class unbiased transformed data set. the parametric and nonparametric part are estimated by the use of ker-nel method based on K-class unbiased transformed data set. Secondly, we obtain the asymptotic normality of parametric estimation and the strong consistency of nonparametric estimation under the common conditions.