On robust Bayesian estimation under some asymmetric and bounded loss function

Abstract

The problem of Bayesian and robust Bayesian estimation with some bounded and asymmetric loss function ABL is considered for various models. The prior distribution is not exactly specified and covers the conjugate family of prior distributions. The posterior regret, most robust and conditional Γ-minimax estimators are constructed and a preliminary comparison with square-error loss and LINEX loss is presented.

Keywords:

• decision theory
• Bayes estimator
• class of priors
• robust Bayesian estimation
• asymmetric bounded loss function

AMS Subject Classification :

• 62 C 10
• 62 F 35
• 62 F 10

Acknowledgements

The authors would like to thank the referee for their suggestions and insightful comments. Supported by Grant MNISW N201 018 3111536.