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:: Volume 2, Issue 1 (8-2008) ::
J. of Stat. Sci. 2008, 2(1): 1-21 Back to browse issues page
Constrained Bayes Estimators under Balanced Loss Functions
Ahmad Parsian , Shahram Azizi Sazi
Abstract:   (18963 Views)

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 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.

Keywords: Balanced and Weighted Balanced Loss Functions, Constrained Bayes Estimators, One-parameter exponential family, Posterior Regret, Posterior Regret Constrained Gamma-Minimax.
Full-Text [PDF 491 kb]   (3335 Downloads)    
Type of Study: Research | Subject: Statistical Inference
Received: 2011/07/4 | Accepted: 2013/08/13 | Published: 2016/06/7
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Parsian A, Azizi Sazi S. Constrained Bayes Estimators under Balanced Loss Functions. J. of Stat. Sci.. 2008; 2 (1) :1-21
URL: http://jss.irstat.ir/article-1-12-en.html

Volume 2, Issue 1 (8-2008) Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences
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