Parametric Estimation Of Regression Model With Contamination Data

Contamination data is a common statistical data in Biological Statistics and Financial Statistics, it is also a incomplete data .There are much factors such as experimental design ,equipment error, restrictions and observers subjective factors,so we are given incomplete data. However, the use of incomplete data is not entirely.Although sometimes we can do a statistical data, but most of the time it is cannot be duplicated, time-consuming too long or the price too is high.Moreover, in the situation which the stationary source has not verified or eliminated,we only obtain the contaminated data.Therefore, the statistical analysis of contamination data have become an important topic. This paper importantly studies the estimation of parameter in regression model which contains contamination data.In chapter one,the problem's background is introduced,including the characteristics and development of regression,the background of contamination data and research at home and abroad.In chapter two,it introduces the estimation of parameter in regression model which contains contamination data under the situation of censord data,including the estimation of contamination coefficients of censord data:one is based on the mean estimate of censord data ,the other is to use the idea to do research on the analysis of regression with censord data;the use of moment estimation method in parametric estimation of broken contamination data;estimation method of semiparametric regression model with contaminated and censord data,and this paper presents the estimations of model parametric and contamination parametric respectively by using least-squares method and moment estimation method.In chaper three,it introduces the estimation method of linear regression model with contaminated data.First,much basic knowledge is introduced.Then,it importantly introduces my perspective : in this paper the estimations of the parameters and coefficient of contamination for the simple regression model and studied when its response variables are contaminated by another random variable sequence it discusses that the interval estimation of posterior confidence probability of parameters on coefficient of contamination by using the method of Bayes inference. And it gives the point estimation of the parameters in the model.As a result of the introduction of priori,it increased the information of estimated parameter, which is useful for improving the performance of the estimates. Application of this method have been a lot of attention to other area.In chaper four, it introduces the estimation method of semiparametric regression model with contaminated data.First , it presents the estimations of model parametric and contamination parametric respectively by using moment estimation method. Then, it importantly introduces my another perspective:we apply (linear) wavelet estimation method to model and give the definition of the unknown parameters to be estimatedβ, unknown function g (? ) and contaminated parameterυ, then prove their weak consistency.When wavelet method is used in regression model, the treatment of conditions that require lower , good nature will be succeed.In last chaper,there are summary and outlook.