ArticleOriginal scientific text
Title
Robust Bayesian estimation in a normal model with asymmetric loss function
Authors 1, 2
Affiliations
- Institute of Applied Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
- Wojciechowskiego 22, 02-495 Warszawa, Poland
Abstract
The problem of robust Bayesian estimation in a normal model with asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.
Keywords
Bayes estimators, asymmetric loss function, robust Bayesian estimation, classes of priors
Bibliography
- B. Betro and F. Ruggeri, Conditional Γ-minimax actions under convex losses, Comm. Statist. Theory Methods 21 (1992), 1051-1066.
- A. Boratyńska, Stability of Bayesian inference in exponential families, Statist. Probab. Lett. 36 (1997), 173-178.
- A. Boratyńska and M. Męczarski, Robust Bayesian estimation in the one-dimensional normal model, Statistics and Decision 12 (1994), 221-230.
- A. DasGupta and W. J. Studden, Frequentist behavior of robust Bayes estimates of normal means, Statist. Decisions 7 (1989), 333-361.
- M. Męczarski, Stability and conditional Γ-minimaxity in Bayesian inference, Appl. Math. (Warsaw) 22 (1993), 117-122.
- M. Męczarski and R. Zieliński, Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior, Statist. Probab. Lett. 12 (1991), 329-333.
- H. R. Varian, A Bayesian approach to real estate assessment, in: Studies in Bayesian Econometrics and Statistics, North-Holland, 1974, 195-208.
- A. Zellner, Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81 (1986), 446-451.