Research On Parameter And Non-parameter Estimate Of Contamination Linear Model

Linear model is one of the most important branches of the statistics, which develops earlier and concludes plentiful theories in mathematical statistics. During the past several hundred years, linear model is not only active in theoretic research areas but also applies widely in some fields such as industry and agriculture meteorology and geology, economical management, medical affairs, educational psychology gradually. As a most popular part in the scientific research in the linear model, contaminated linear model is the focus because of the widespread existence in actual life and has the very high value in the application.The thesis is a research on non-parameter estimate of contamination data for simple linear regression model. In the first part of this paper, we suggest the history about the progress of the contaminated linear model and give a brief summary about the whole paper. The second part and third part of this paper is the main body. We suggest three different discussion results about the three different contaminated models which have been brought up in the preface. In the second part, we give the estimation about the parameters of Model I and Model II with both the moment method and the maximum likelihood method. In the third part, we consider the contaminated linear model: y_i =βx_i+e_i, i = l,2,…,n.Let the errors sequence {e_i} is a stationary with unknown density f(x). We obtain consistency the kernel estimation of f(x) based on the residuals. Then we establish nonparametric estimation in contaminated coefficientεand regression parameterβ. We prove the strong consistency and convergence rate almost surely of the estimators.The fourth part of this paper is the applications. In this part we analyze the actual of the contaminated model by three different examples. These examples discuss the MLE of the contaminated model, the non-parametric fitting of the contaminated model and the simulation on coefficient of contamination.