Linear Bayes estimator for the two-parameter exponential family under type II censoring

For the two-parameter exponential family, a linear Bayes method is proposed to simultaneously estimate the parameter vector consisting of location and scale parameters. The superiority of the proposed linear Bayes estimator (LBE) over the classical UMVUE is established in terms of the mean square error matrix (MSEM) criterion. The proposed LBE is simple and easy to use compared with the usual Bayes estimator, which is obtained by the MCMC method. Numerical results are presented to verify that the LBE works well. In the empirical Bayes framework, the paper invokes a linear empirical Bayes estimator (LEBE) by using a linear combination of historical samples. It is shown under some mild regularity conditions that the LEBE is superior to the classical UMVUE and the maximum likelihood estimator in terms of MSEM. It is further shown with numerical results that the performance of LEBE gets better with the increase in the number of historical samples.