Research On Property Of The Almost Unbiased Estimator For Parameters In The Linear Models

The study of parameter estimation in linear model has always been a hot topic,and the least squares estimate is the earliest estimate.However,with the emergence of multiple co-linear phenomena,the least square estimation is no longer a good estimate.Many biased estimates have been proposed to replace the least squares estimator,such as Stein estima-tion,ridge estimation,Liu estimation,etc.Because the biased estimates deviate from the the true value of the parameter,people proposed the almost unbiased estimator,such as al-most unbiased ridge estimation,almost unbiased Liu estimation,almost unbiased estimate of two parameters,almost unbiased Stein ridge principal component estimation.Although the almost unbiased estimation is still biased estimation,it has a smaller skewness than the corresponding biased estimations.In this paper,we study the almost unbiased estimator for parameters in linear model,many scholars have studied the nature of almost unbiased estimates,compare it with least squares estimates or some biased estimates.Based on the previous research,this paper makes further research on it and mainly does the following work:In the first place,the linear model and the development of some estimates are intro-duced briefly in the introduction.The second chapter mainly studies the properties of almost unbiased estimations under the criterion of mean square error matrix,Bayes linear unbiased minimum variance estimation is batter than almost unbiased ridge estimation and almost unbiased Liu estimation.The third chapter also discusses the properties of almost unbiased estimations under the criterion of mean square error matrix,in given conditions,some suffi-cient and necessary conditions for the almost unbiased Stein ridge type principal component estimator being batter than the almost unbiased Liu estimation,the almost unbiased Liu estimation being batter than the almost unbiased Stein ridge type principal component esti-mator,the almost unbiased Stein ridge type principal component estimator being batter than the almost unbiased two-parameter estimation,the almost unbiased two-parameter estima-tion being batter than the almost unbiased Stein ridge type principal component estimator,respectively.