Research Of Preliminary Test Estimators For Error Variance In Linear Model

Linear model is a kind of important model in modern statistics,which is widely used in economy,finance,engineering technology,and so on.In the process of modeling analysis,statisticians mainly discuss parameter estimation,hypothesis test and prediction of the future observations in the parametric regression models.In comparison,prediction of the future observations and hypothesis test are mostly depended on the result of parameter estimation.Therefore,estimation of parameter plays an important role in the process of modeling analysis,and it is paid high attention to statisticians.In this paper,we main discuss the superiority of the preliminary test estimators for error variance in a linear model based on W,LR and LM tests.Firstly,in the normal linear model,we consider the preliminary test estimators for error variance based on W,LR and LM tests,respectively.Meanwhile,we get the explicit expression of risk function of each estimator and analyze the optimal property of three estimators.We obtain the optimum conditions of each estimator based on theoretical analysis and numerical calculation methods.Secondly,Since the error of linear models in economical and financial problems usually obeys a multivariate t distribution,we further propose preliminary test estimators for error variance based on W,LR and LM tests by combining the statistical properties of three test statistics with multivariate t errors.Meanwhile,we inspect the risk performance of each estimator in theory.Moreover,we illustrate the theoretical results by numerical computation and simulation analysis.Finally,the research contents of this paper are summarized,and the future work is prospected.