Robust Bayesian estimation in a normal model with asymmetric loss function

Agata Boratyńska; Monika Drozdowicz

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 1, page 85-92
  • ISSN: 1233-7234

Abstract

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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.

How to cite

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Boratyńska, Agata, and Drozdowicz, Monika. "Robust Bayesian estimation in a normal model with asymmetric loss function." Applicationes Mathematicae 26.1 (1999): 85-92. <http://eudml.org/doc/219227>.

@article{Boratyńska1999,
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.},
author = {Boratyńska, Agata, Drozdowicz, Monika},
journal = {Applicationes Mathematicae},
keywords = {Bayes estimators; asymmetric loss function; robust Bayesian estimation; classes of priors; asymmetric loss functions},
language = {eng},
number = {1},
pages = {85-92},
title = {Robust Bayesian estimation in a normal model with asymmetric loss function},
url = {http://eudml.org/doc/219227},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Boratyńska, Agata
AU - Drozdowicz, Monika
TI - Robust Bayesian estimation in a normal model with asymmetric loss function
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 1
SP - 85
EP - 92
AB - 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.
LA - eng
KW - Bayes estimators; asymmetric loss function; robust Bayesian estimation; classes of priors; asymmetric loss functions
UR - http://eudml.org/doc/219227
ER -

References

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  1. [1] B. Betro and F. Ruggeri, Conditional Γ-minimax actions under convex losses, Comm. Statist. Theory Methods 21 (1992), 1051-1066. Zbl0800.62043
  2. [2] A. Boratyńska, Stability of Bayesian inference in exponential families, Statist. Probab. Lett. 36 (1997), 173-178. Zbl0893.62017
  3. [3] A. Boratyńska and M. Męczarski, Robust Bayesian estimation in the one-dimensional normal model, Statistics and Decision 12 (1994), 221-230. Zbl0802.62032
  4. [4] A. DasGupta and W. J. Studden, Frequentist behavior of robust Bayes estimates of normal means, Statist. Decisions 7 (1989), 333-361. Zbl0685.62004
  5. [5] M. Męczarski, Stability and conditional Γ-minimaxity in Bayesian inference, Appl. Math. (Warsaw) 22 (1993), 117-122. Zbl0789.62007
  6. [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. [7] H. R. Varian, A Bayesian approach to real estate assessment, in: Studies in Bayesian Econometrics and Statistics, North-Holland, 1974, 195-208. 
  8. [8] A. Zellner, Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81 (1986), 446-451. Zbl0603.62037

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