The Bayes Rule Of The Scale Parameter Of The Hierarchical Inverse Gamma And Inverse Gamma Model Under Stein's Loss

In this thesis,the Bayesian estimation of the scale parameter of the hierarchical inverse gamma-inverse gamma model under Stein's loss is studied.For the scale parameter of the hierarchical inverse gamma and inverse gamma model,we analytically calculate its Bayes posterior estimator under Stein loss and its posterior expected Stein's loss.At the same time,we calculate the Bayes posterior estimator and the posterior expected Stein's loss(PESL)under the square error loss.Through theoretical deduction and data simulation,it is proved that the Bayes posterior estimator and the Bayes posterior expected loss under the square error loss function are both larger than those under the Stein loss function.Empirical Bayes estimators of the scale parameter of the hierarchical inverse gamma and inverse gamma model are also calculated by moment method and Maximum Likelihood Estimation(MLE)method.The consistencies of moment estimator and MLE are demonstrated by numerical simulation.At the same time,the goodness-of-fit tests are carried out for the simulated data with known parameters and unknown parameters respectively.The results show that all cases have passed the tests,and the test effect of MLE is better than that of moment estimation.Finally,empirical Bayes estimates of total liabilities of Chinese industrial enterprises are calculated.This thesis mainly consists of the following 5 parts: The chapter 1 is an introduction,which introduces the current situation of Bayesian estimation.Chapter 2 is the main conclusion,which mainly introduced the Bayes posterior expected loss and empirical Bayes estimators of the scale parameter.Chapter 3 is numerical simulation,which illustrate the consistencies of moment estimation and the MLE,the goodness-of-fit of the model,and also calculate Bayes posterior estimates and PESL of simulated data.Chapter 4 is a real data example.The chapter 5 is the conclusion and prospects,which summarizes the main work of this thesis and prospects.