Stein Root Root Estimators Of The Parameters In Linear Regression Model

In this paper, we do some research in the linear regression model. When thedesign matrix is ill-conditioned, the result of least squares estimators is not so good oreven worse. Therefore, under the meaning of MSE, we propose a class of newestimators by combining the root root estimator and the Stein estimator.Firstly, for the usual linear regression model, we give the definition of Stein rootroot estimators, getting the expression of its MSE. Under the criterion of MSE, it isproved that Stein root root estimators are better than the least square estimators, rootroot estimators and Stein estimators when they are satisfies with different sufficientconditions. Through an example of simulation, it is confirmed that the MSE of Steinroot root esimators is less than that of the least squares estimators, the root rootestimators and the Stein estimators.Secondly, considering linear regression model with the restricted conditionR β=0, we gain the Stein root root estimator with the restricted condition, talkingover its several statistical propertie and proving independently sufficient conditionsexisted that both restricted root root estimator and restricted Stein estimator’s MSEare more than restricted Stein root root estimator’s MSE.Finally, on the base of the Chapter three, we consider about the usual linearregression model. Furthermore, through replacing the root parameter k by diagonalmatrixK=diag(k1, k2, L, kp), we obtain the expression of estimator-gereralized Steinroot root estimators. After discussing a sepcial kind of estimator-gereralized Steinroot root estimators and having a sufficient condition that it more efficient thanordinary Stein root root estimator, it goes deep into the research of the ordinaryestimator-gereralized Stein root root estimators. Under the criterion of MSE, it isgiven that the estimator is more efficient than estimator-gereralized root rootestimators and Stein estimators in independently sufficient conditions.