正态总体误差方差的经验Bayes估计及其优良性

The empirical Bayes estimation and its superiority for error variance in normal distribution

对正态总体误差方差在共轭先验分布和加权平方损失下导出了其Bayes估计,构造了其参数型经验Bayes(PEB)估计,研究了其在均方误差(MSE)准则下相对于一致最小方差无偏估计(UMVUE)的优良性.当先验分布中的超参数完全未知时,通过数值模拟比较了PEB估计和UMVUE的均方误差,获得了PEB估计的优良性.

Abstract： Under the conjugate prior distribution of the error variance in normal distribution and the weighted squared error loss function, the Bayes estimator was derived and the parametric empirical Bayes （PEB） estimator was constructed for the error variance. The superiority of the PEB estimation over the uniformly minimum variance unbiased estimation （UMVUE） in terms of the mean-square error （MSE） criterion was studied. In the case where the hyper-parameters of the prior distribution are completely unknown, the superiority of the PEB estimation over be UMVUE under the MSE criterion wasinvestigated with a simulation study.