The Empirical Bayes Estimators Of The Parameter Of The Hierarchical Uniform And Inverse Gamma Model Under Stein's Loss

This paper is mainly to estimate the Bayes estimators of the parameter of the hierarchical uniform and inverse gamma model under Stein's loss.First,we calculate the Bayes posterior estimator of the hierarchical uniform and inverse gamma model under the squared error loss or Stein's loss function and the corresponding Posterior Expected Stein's Loss(PESL).After theoretical calculations,we can see that PESL depends only on ? and n,and the Bayes estimator and the PESL under Stein's loss are unanimously smaller than those under the squared error loss.Moreover,we obtain the empirical Bayes estimators of the parameter of the uniform distribution with a conjugate inverse gamma prior by the two methods of moment estimation and maximum likelihood estimation.In numerical simulations,we have illustrated three things: The two inequalities of the Bayes posterior estimators and the PESLs under the squared error loss or Stein's loss function;the moment estimators and the Maximum Likelihood Estimators(MLEs)are consistent estimators of the hyperparameters;the goodness-of-fit of the model to the simulated data.The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters.Finally,the above theoretical research is illustrated by the current prices of the SZSE 300 on March4,2019.