Robust Bayesian estimation in a normal model with asymmetric loss function

• Autorzy: Agata Boratyńska , Monika Drozdowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bayes estimators; asymmetric loss function; robust Bayesian estimation; classes of priors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1999
• Tom: 26
• Numer: 1
• Strony: 85-92

Daty

wydano

1999

otrzymano

1998-09-02

poprawiono

1998-12-03

Twórcy

autor

Agata Boratyńska

• Institute of Applied Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Monika Drozdowicz

• Wojciechowskiego 22, 02-495 Warszawa, Poland

Bibliografia

• [1] B. Betro and F. Ruggeri, Conditional Γ-minimax actions under convex losses, Comm. Statist. Theory Methods 21 (1992), 1051-1066.
• [2] A. Boratyńska, Stability of Bayesian inference in exponential families, Statist. Probab. Lett. 36 (1997), 173-178.
• [3] A. Boratyńska and M. Męczarski, Robust Bayesian estimation in the one-dimensional normal model, Statistics and Decision 12 (1994), 221-230.
• [4] A. DasGupta and W. J. Studden, Frequentist behavior of robust Bayes estimates of normal means, Statist. Decisions 7 (1989), 333-361.
• [5] M. Męczarski, Stability and conditional Γ-minimaxity in Bayesian inference, Appl. Math. (Warsaw) 22 (1993), 117-122.
• [6] 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.
• [7] H. R. Varian, A Bayesian approach to real estate assessment, in: Studies in Bayesian Econometrics and Statistics, North-Holland, 1974, 195-208.
• [8] A. Zellner, Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81 (1986), 446-451.