TY - JOUR T1 - Constrained Bayes Estimators under Balanced Loss Functions TT - برآوردگرهای بیزی مقید تحت توابع زیان متعادل JF - JSS JO - JSS VL - 2 IS - 1 UR - http://jss.irstat.ir/article-1-12-en.html Y1 - 2008 SP - 1 EP - 21 KW - Balanced and Weighted Balanced Loss Functions KW - Constrained Bayes Estimators KW - One-parameter exponential family KW - Posterior Regret KW - Posterior Regret Constrained Gamma-Minimax. N2 - 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-parameter exponential families of distributions. A common approach to the prior uncertainty in Bayesian analysis is to choose a class $Gamma$ of prior distributions and look for an optimal decision within the class $Gamma$. This is known as robust Bayesian methodology. Among several methods of choosing the optimal rules in the context of the 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. M3 ER -