Bayes Linear Unbiased Minimum Variance Estimator In Linear Model And Its Small Sample Properties

In statistics,linear model is a simple and widely used model,which has been wide-ly used in important fields,such as business,industry and economics.When we study the linear model,the first consideration is the parameter estimates.And then,the least squares estimates was put forward earliest.However,with the development of statistical theory and the increasing number of variables,The mean square error(MSE)would get bigger,the research in the fields of practical problems will appear large deviation.To solve this prob-lem,people put forward Bayes linear unbiased minimum variance estimation and a series of biased estimation,such as Stein estimation,James-Stein estimation,ridge estimation,Liu estimation,and so on.This paper study the parameter estimation problem in linear model.In the past,many scholars have studied the properties of the Bayes linear unbiased minimum variance estima-tion.Furthermore,they have compared it with the least squares estimation,generalized least squares estimation,ridge estimation and others.While in this paper,on the basis of their research,we will discuss Bayes linear unbiased minimum variance estimation and its small sample properties.It consists of the following sections:First,the introduction describes the basic knowledge of linear model and the devel-opment process of several common estimations,including Bayes linear unbiased minimum variance estimation.The second chapter will discusse Bayes linear unbiased minimum vari-ance estimation under generalized mean square error,compare it with Liu estimation and James-Stein estimation and give the proof.The third chapter will continue to discuss the nature of Bayes linear unbiased minimum variance estimation,also compare it with Liu es-timation and James-Stein estimation.