Robust Bayes Estimation

Abstract

This article deals with robust Bayes estimation, namely Stable action, Conditional Gamma-Minimax action and Posterior Regret Gamma-Minimax action. We extend the results of Meczarski (1993) and obtain the exact actions in each case. The results are applied for a family of one-parameter exponential families introduced by Morris (1983) as an extension of the results of Boratynska (1997).

Keywords:

• Bayes action
• Class of prior distributions
• Conditional Gamma-Minimax
• Posterior Regret Gamma-Minimax
• Robust bayes analysis
• Stable action

Mathematics Subject Classification:

• Primary 62C10, 62C20
• Secondary 62F10, 62F15, 62F35

Acknowledgements

The research of A. Parsian was supported by a grant of the Research Council of the University of Tehran.