Pitman Superiority Of United Biased Estimation

In the linear regression model, the least square estimation has lots of goodperformance. However, with the deepening of the study, scholars discover that leastsquare estimation shows apparently disadvantage, the linear biased estimation is seen asthe most effective method in ameliorating the least square estimation. The united biasedestimation includes ridge estimation, James-Stein estimation, Liu estimation and manyother important estimation. In recent years, due to the high generalization andpracticability, the united biased estimation has been widely used.The emergence of different estimate models is bound to bring about thecomparison of them, Pitman criterion was proposed by Pitman in1937which was usedto compare the parameter estimations. Since1980s, it has been received scholars’ greatattention. In this paper, we further study the superiority of parameter estimation in linearregression model under the pitman criterion.First of all, we studied the superiority of two united biased estimation under thepitman criterion, and on this basis, respectively discusses the superiority of Liuestimation, ridge estimation, principal components estimation, James-Stein estimationand least square estimation. Then, under the pitman criterion, we compared thesuperiority between ridge estimation and James-Stein estimation, and proved that ridgeestimation is superior to James-Stein estimation under certain condition. Finally, wefurther demonstrate the superiority of both united biased estimation and James-steinestimation under the pitman criterion,and obtain the sufficient conditions under whichthe united biased estimation outperform James-stein estimation under the pitmancriterion.