Study On Generalized Ridge Estimator Of Regression Coefficients In Linear Model

The paper studies the generalized ridge estimator of regression coefficients in linear regression model,and discusses its superiorities and relative efficiencies.The paper is divided into four chapters.In the first chapter,the studying situation of linear regression model and its parameter estimators are introduced,especially the recent studying of the generalized ridge estimator.In the second chapter,we give some mathematical symbols used in the paper,and give the definitions of the generalized ridge estimator,linear regression model and its normalized form.In the third chapter,the property of the generalized ridge estimator under the mean square error matrix(MSEM) criterion is studied,and a necessary and sufficient condition of it being better than the least square estimator is given.At the same time,the third chapter also makes some discussions for the superiority of the generalized ridge estimator over the least square estimator under Pitman Closeness criterion,and gains a precise conclusion.Finally,the fourth chapter researches several relative efficiencies of the generalized ridge estimator over the least square estimator,and discusses their relations in detail.