A Further Study On Two Parameter Estimation In Lnear Model

In the classical linear model,the least squares estimation of the parameters is no longer a good estimate due to the existence of the Stein phenomenon,and the improvement of the least squares estimation has been a hot topic in the theory and application.Biased estimation and taking into account the priori information about parameter in the sample information are two of the more common improvement methods.Further,the statisticians propose an almost unbiased estimate of the concept from the perspective of reducing the deviation of the biased estimator.On the basis of predecessors' research,this paper studies the parameter estimation considering the a priori information in the linear model.On the other hand,we use the almost unbiased idea to deal with the estimation of the two parameters to get a new estimate,The superiority of parameter estimation is further studied.Firstly,considering the priori information,a new modified two-parameter estimate is obtained by constructing the convex function about the least squares estimation and the priori information according to the previous research ideas.The new estimate also is the generalization of the least squares estimation,the modified ridge estimate,the modified Liu estimate,then the sufficient conditions for the new estimators to be better than those of the estimators are given in the sense of the mean square error matrix criterion.Secondly,using the almost unbiased idea,we propose a new almost unbiased two-parameter estimate.The new estimate is a generalization of the least squares estimation,almost unbiased ridge estimation and almost unbiased Liu estimation.Under the criterion of the mean square error matrix,the paper presents the sufficient conditions for the new estimation over the least squares estimation,almost unbiased ridge estimation,almost unbiased Liu estimation and another almost unbiased two-parameter estimate.The theoretical results are proved by data simulation.At the same time,the revised estimate of the estimate is taken into account.