Comparison Of The Risk Of Generalized Ridge Estimator And Stein Estimatorin Linear Regression Model

Linear regression model is very important in the statistics,and it has a wide application in insurance.The parameters estimation problems in the model is the focus study of the scholars for many years,the least squares estimate with its excellent properties is widespread paid attention to.But,as the research gradually developed,the least squares estimate appeared many problems,such as,when the design matrix is a singular matrix,there will be a larger mean square error of least squares estimate,so the accuracy and deviation of the estimation are affected.Therefore,statistics of the researchers put forward biased estimate,to improve a balance of accuracy and deviation of the estimation.In view of the linear regression model,this paper studies biased estimation of the parameters.Previously,scholars mainly aimed at the risk comparisons of biased estimation and least squares estimation,this article is mainly to the risk comparisons of the generalized ridge estimators and Stein estimators.First,in the introduction: This paper briefly introduces the research background and significance of the generalized ridge estimators and Stein estimators,and the application of regression in insurance.The second chapter: It briefly introduces the basic knowledge of linear regression model and the least squares estimate,and the development of several biased estimate,which mainly introduces the generalized ridge estimators and Stein estimators.The third chapter: under the generalized mean square error criterion,mainly discusses respectively the risk of the comparison between generalized ridge estimation and Stein estimation,and then gives the proofs.The fourth chapter: On the basis of the balanced loss function,mainly discussesrespectively the risk of the comparison between generalized ridge estimation and Stein estimation,and then gives the proofs,and then discusses the effect of the weight the balanced loss function.