MSE Performance Of PT-2SHI Estimator In A Linear Model When Relevant Regressors Are Omitted

The biased estimation is a kind of important estimation method in parameter estimation,which has important theoretical and practical value.In the linear model,compared with the unbiased estimation,the biased estimation can obtain smaller estimated mean square error and predicted mean square error after sacrificing the unbiased estimation.If the classical hypothesis is not satisfied,the performance of biased estimation methods is much better to the classical unbiased estimation methods.In the 1950s and 1960s,Stein and James(1955,1961)first proposed a shrinkage estimation method,named SR estimation.Since then,a large number of scholars have conducted statistical research in this field,leaving a wealth of research results.At the beginning of this century,Namba(2000)combined two classical shrinkage estimation methods,SR estimation method and 2SHI estimation method through pre-testing ideas,and constructed a new pre-test estimation method.Namba named this new estimation method PT-2SHI estimation.Namba compares the PT-2SHI estimation method with the classical SR estimation method and PSR estimation method by mathematical proof and numerical analysis methods,and demonstrates the mean square error advantage of the PT-2SHI estimation.This paper has carried out further research on the PT-2SHI estimation.First of all,this paper proves in the mathematical theory that the PT-2SHI estimation still dominates the classical SR estimator in a model when relevant regressors are omitted.Then,the numerical analysis method is used to further verify the result,and the setting of the characteristic parameters of the PT-2SHI estimator is studied.Finally,the minimum and maximum regret criteria are introduced.Under the guidance of the guidelines,new insights are given to the selection of the pre-test thresholds for PT-2SHI estimation.