Two Classes K-d Rank Estimation Of Parameter In Linear Regression Models

In this paper,we consider the following linear regression models yi=X(?)?+?i,i=1,2…n,Among them,yi is the observed value of the response variable,Xi is the observation of p-dimensional explanatory variable,and the regression coefficient ? is the p-dimensional unknown parameter vector.The linear regression model is widely used in the fields of medical treatment,finance,national defense and so on.Therefore,the research on it has practical significanceOn the basis of Liu rank estimation,we propose k-d rank estimation and constrained k-d rank estimation,PT(k,d)rank estimation,S(k,d)rank estimaotin and S+(k,d)rank estimation.We generalize rank-based least squares estimation,ridge estimation,Liu estima-tion,PT-Liu estimation,S-Liu estimation and S+-Liu estimation.Then,in the sense of asymptotically distributed risk,the superiority of each estimator is obtained by comparing each estimator under certain conditions.Our conclusion is verified by simulation and applied in the exampleIn chapter 2,on the basis of rank estimation,the k-d rank estimation of linear regression model is proposed,and the rank-based least squares estimation,ridge estimation and Liu estimation are generalized.In the sense of asymptotic distribution risk,the advantages and disadvantages of the new estimator are compared with the least squares rank estimation,ridge rank estimation and Liu rank estimation,and the sufficient conditions for the new estimator to be superior to the least squares rank estimation,ridge rank estimation and Liu rank estimation are obtainedIn chapter 3,based on the k-d rank estimation and Score test of linear regression model,the PT(k,d)rank estimation.S(k,d)rank estimation and S+(k,d)rank estimation are proposed.Then,in the sense of asymptotically distributed risk,the PT(k,d)rank estimation,S(k,d)rank estimation and k-d rank estimation,S+(k,d)rank estimation and constrained k-d rank estimation are compared to demonstrate the superiority of the new estimation under certain conditionsIn chapter 4,a simulation example is given to verify the superiority of the proposed estimator and the application in the example.