Two Classes Of Almost Unbiased Estimators In Linear Model

In this paper,we focus on the existence of complex collinearity in general linear models and linear models with equality linear restriction.Two new classes of almost unbiased estimators are proposed and their properties are discussed.The specific content is:First,in the general linear model,a new class of almost unbiased estimator,that is,almost unbiased two-parameter principal component estimator,is proposed in combination with almost unbiased two-parameter estimator and principal component estimator.And in the sense of mean square error matrix,the superiority of almost unbiased two-parameter principal component estimator is discussed.Necessary and sufficient conditions for the estimation is better than least squares estimator,almost unbiased ridge estimator,almost unbiased Liu estimator,almost unbiased ridge-type principal component estimator,almost unbiased Liu-type principal component estimator,and almost unbiased two-parameter estimator.At the same time,the theoretical results are illustrated by empirical analysis and Monte Carlo simulation analysis.Secondly,in the linear model with equality linear restriction,a class of almost unbiased two-parameter principal component estimator is proposed.The superiority of the almost unbiased two-parameter principal component estimator in the sense of mean square error matrix and mean square error are discussed respectively.In the sense of the mean square error matrix,the necessary and sufficient conditions for the estimation to be better than the restricted least squares estimator,the restricted almost unbiased ridge estimator,the restricted almost unbiased two-parameter estimator and the new restricted almost unbiased two-parameter estimator are obtained.At the same time,the performance of the almost unbiased two-parameter principal component estimator is explained by empirical and simulation analysis in the sense of mean square error.Thirdly,based on the mean square error matrix and the mean square error,theproperties of the two classes of almost unbiased estimators proposed in this paper are compared and analyzed.The necessary and sufficient conditions for the restricted almost unbiased two-parameter principal component estimator in the sense of the mean square error matrix are better than the almost unbiased two-parameter principal component estimator,and the significance of the mean square error for the two classes of almost unbiased estimator is obtained through empirical and simulation analysis.Finally,the work of this paper is summarized,and the direction that future research can be considered is pointed out.