E-Bayesian estimations of parameter and its evaluation standard: E-MSE (expected mean square error) under different loss functions

Abstract

This paper is concerned with using the E-Bayesian method for computing estimates of Pareto index. In order to measure the estimated error, in the case of the one hyper parameter, the definition of E-MSE (expected mean square error) is proposed based on the definition of E-Bayesian estimation. Moreover, the formulas of E-Bayesian estimation and formulas of E-MSE are given respectively, these estimations are derived based on a conjugate prior distribution under different loss functions (including: squared error loss, weighted squared error loss and precautionary loss). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation, results are compared on basis of E-MSE. Finally, combined with the golfers income problem are performed to calculated (also using OpenBUGS), and for income inequality degree were performed to compared and analyzed. When considering evaluating the E-Bayesian estimations under different loss functions, this paper proposed the E-MSE as evaluation standard.

Keywords:

• E-Bayesian estimation
• E-MSE
• Pareto index
• Monte Carlo simulation
• income inequality

MR(2010) Subject Classification:

• 62F15
• 62F10

Acknowledgments

The author wishes to thank Professor Xizhi Wu, who checked the paper and gave author very helpful suggestions. The author is very grateful to the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this paper.

Additional information

Funding

This work was supported by Zhejiang Province Natural Science Foundation [No. LY18A010026].