基于W,LR和LM检验的误差方差预检验估计的比较  

Comparisons Among Preliminary Test Estimators for Error Variance Based on W,LR and LM Tests

作　　者：胡桂开 桂洋明 彭萍 HU Guikai;GUI Yangming;PENG Ping(School of Science,East China University of Technology,Nanchang 330013,China)

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《应用数学》2020年第2期308-317,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11661003);the Natural Science Foundation of Jiangxi Province(20161BAB201033,20192BAB201006);Science and Technology Project of Education Department of Jiangxi Province(GJJ150582,GJJ160559)。

摘　　要：本文研究多元t分布模型中误差方差分别基于W,LR和LM检验的预检验估计问题.首先,分别获得了基于三个大样本检验的预检验估计和对应的风险;其次,基于理论分析和数值分析的方法得到了各个估计的优良表现,结果表明预检验估计的风险在检验临界值为1时达到最小,并得到了各个估计保持最优的条件;最后,通过自助模拟的方法进一步分析了各个估计的优良性,所得结果和理论分析是一致的.In this paper,three preliminary test estimators for error variance based on W,LR and LM tests with multivariate t errors are considered.Firstly,pre-test estimators based on three large sample tests and their risks are derived,respectively.Secondly,the risk performances are discussed by theoretical and numerical analysis,respectively.It is shown that the risks of preliminary test estimators attain the smallest value when the critical value of test is one.Moreover,the conditions for each pre-test estimator to be optimal are obtained.Finally,we further give a bootstrap method to analyze the superiority of proposed estimators.

关 键 词：预检验估计 误差方差 等式约束 多元T分布 

分 类 号：O212.4[理学—概率论与数理统计]