On robust Bayesian estimation under some asymmetric and bounded loss function

References

• Leon , R. W. and Wu , C.-F. J. 1992 . A theory of performance measures in parameter design . Statist. Sinica , 2 : 335 – 358 .
   Web of Science ®Google Scholar
• Tribus , M. and Szonyi , G. 1989 . An alternative view of the Taguchi approach . Quality Progress , 22 : 46 – 52 .
   Google Scholar
• Varian , H. R. 1974 . “ A Bayesian approach to real estate assessment ” . In Studies in Bayesian Econometrics and Statistics 195 – 208 . North-Holland
   Google Scholar
• Berger , J. O. 1985 . “ Statistical Decision Theory and Bayesian Analysis ” . New York : Springer Verlag .
   Google Scholar
• Wen , D. and Levy , M. S. 2001 . BLINEX: a bounded asymmetric loss function with application to Bayesian estimation . Commun. Statist. – Theory Meth. , 30 ( 1 ) : 147 – 153 .
   Web of Science ®Google Scholar
• Towhidi , M. and Behboodian , J. 2002 . Minimax estimation of a bounded parameter under some bounded loss functions . Far East J. Theo. Stat. , 6 : 39 – 48 .
   Google Scholar
• Sivaganesan , S. and Berger , J. O. 1989 . Ranges of posterior measures for priors with unimodal contamination . Ann. Statist. , 17 ( 2 ) : 868 – 889 .
   Web of Science ®Google Scholar
• Das Gupta , A. and Studden , W. J. 1989 . Frequentist behavior of robust Bayes estimates of normal means . Statist. Decision , 7 : 333 – 361 .
   Google Scholar
• Betro , B. and Ruggeri , F. 1992 . Conditional Γ-minimax action under convex losses . Comm. Statist. Theory Methods , 21 : 1051 – 1066 .
   Web of Science ®Google Scholar
• Rios Insua , D. , Ruggeri , F. and Vidakovic , B. 1995 . Some results on posterior regret Γ-minimax estimation . Statist. Decision. , 13 : 315 – 331 .
   Google Scholar
• Mçczarski , M. and Zieliński , R. 1991 . Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior . Statist. Probab. Lett. , 12 : 329 – 333 .
   Google Scholar
• Spiring , F. A. 1993 . The reflected normal distribution . Can. J. Statist. , 3 ( 21 ) : 321 – 330 .
   Google Scholar
• Wen , D. and Levy , M. S. 2001 . Admissibility of Bayes estimates under BLINEX loss for the normal mean problem . Commun. Statist. – Theory Meth. , 30 ( 1 ) : 155 – 163 .
   Web of Science ®Google Scholar
• Zellner , A. 1986 . A Bayesian estimation and prediction using asymmetric loss function . J. Am. Statisti. Assoc. , 81 ( 394 ) : 446 – 51 .
   Web of Science ®Google Scholar
• Jafari Jozani , M. , Nematollahi , N. and Shafie , K. 2002 . An admissible minimax estimator of a bounded scale parameter in a subclass of the exponential family under scale-invariant squared-error loss . Statist. Probab. Lett. , 60 : 437 – 444 .
   Web of Science ®Google Scholar
• Karatsuba , E. A. 2000 . On the asymptotic representation of Euler gamma function by Ramanujan . J. Comput. Appl. Math. , 135 : 225 – 240 .
   Google Scholar
• Anderson , G. D. and Qiu , S.-L. 1997 . A monotonicity property of the gamma function . 125 ( 11 ) : 3355 – 3362 . Proc. AMS
   Google Scholar
• Arias-Nicolás , J. P. , Martin , J. , Ruggeri , F. and Suárez-Llorens , A. 2008 . Optimal actions in problems with convex loss function . Int. J. Approx. Reason. , doi:10.1016/j.ijar.2008.03.014
   PubMedGoogle Scholar
• Ruggeri , F. and Sivaganesan , S. 2000 . On a global sensitivity measure for Bayesian inference . Sankhyá Ser. A. , 17 ( 1 ) : 110 – 127 .
   Google Scholar
• Boratyńska , A. 2002 . Robust Bayesian estimation with asymmetric loss function . Appl. Math. , 29 ( 3 ) : 297 – 306 .
   Google Scholar