Some Research On Regression Model With Censored Data

Regression analysis is a statistical method of dealing with statistical correlations of some variables. In theory, regression functions are usually unknown, and regression analysis is to estimate regression function according to the value of covariate and response variable. The choosing of regression method largely depends on the assumption of regression model. Linear regression model is the one which is oldest, mostly applied and has plenty of related mature theory. But we usually have to use nonparametric regression model because the assumption of linear regression model cannot be satisfied in actual application. Then there appears many new models, such as semiparametric model, generalized linear model, vary-coefficient model and so on.Regression theory under complete data is mature, but it always appears censored data in some fields, such as biology science,clinial experiment and quality control. This paper is to do some research on the estimation of linear regression model, nonparametric model and semiparametric model under different kinds of errors . To sum up, the works and innovations of this thesis could be summarized as follows:1. We use two methods to estimate linear regression parameters under interval -censored covariate. Firstly, baesd on the maximum estimator of the parameter in distribution of covariate, we construct the interval conditional mean of the censored covariates. Then the estimators of regression parameters are obtained and the asymptotic unbiasness and consistency of our proposed estimators are proved. Secondly, we propose a two-step iterative algorithm: When regression parameters are given, parameters in the distribution of covariates are obtained to maximize the likelihood function of interval-censored covariates; when distribution parameters are given, regression parameters are obtained based on conditional mean of covariates using least square method. Simulation shows the performance is good.2. We propose local linear estimators of nonparametric regression model under interval-censored covariate. We analyze the influence on the estimator by the deviation between censored data and the real value, then amend the censored data . Based on the amended data, we get the final local linear estimators. The good performance of our proposed estimators is illustrated by some simulation examples.3. For semiparametric regression model with randomly censored data, we propose the estimators of parametric and nonparametric part by the use of the nearest neighbor method based on distribution function and least squares methods, using the idea of two-step estimation. The asymptotic normality of parametric part and the strong consistency of nonparametric part are proved under some weak conditions.4. For semiparametric regression model with censored data under NA errors, we propose the estimators of parametric and nonparametric part. By the use of convergence property of sums of NA sequences, the o(n~-1/4) convergence rate of parametric part and the strong consistency of nonparametric part are proved. We also obtain the asymptotic normality of parametric part.