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

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 the UMVUE under the MSE criterion was investigated with a simulation study.