برآورد گرهاي بيزي مقيد تحت توابع زيان متعادل

Constrained Bayes Estimators under Balanced Loss Functions

In this paper, a new class of estimators namely Constrained Bayes Estimators are obtained under Balanced Loss Function (BLF) and Weighted Balanced Loss Function (WBLF) using a "Bayesian solution". The Constrained Bayes Estimators are calculated for the natural parameter of one-paraineter exponential families of distributions. A common approach to the prior uncertainty in Bayesian analysis is to choose a class T of prior distributions and look for an optimal decision within the class T. This is known as robust Bayesian methodology. Among several methods of choosing the optimal rules in the context of robust Bayes method, we discuss obtaining Posterior Regret Constrained Gamma-Minimax (PRCGM) rule under Squared Error Loss and then employing the "Bayesian solution", we obtain the optimal rules under BLF and WBLF.