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Robustness of Bayes decisions for normal and lognormal distributions under hierarchical priors

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  • Sinha, Pankaj
  • Jayaraman, Prabha

Abstract

In this paper we derive the Bayes estimates of the location parameter of normal and lognormal distribution under the hierarchical priors for the vector parameter, . The ML-II ε-contaminated class of priors are employed at the second stage of hierarchical priors to examine the robustness of Bayes estimates with respect to possible misspecification at the second stage. The simulation studies for both normal and lognormal distributions confirm Berger’s (1985) assertion that form of the second stage prior does not affect the Bayes decisions.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22416.

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Date of creation: 30 Apr 2010
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Handle: RePEc:pra:mprapa:22416

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Keywords: Hierarchical Bayes; Hierarchical priors; ML-II ε-contaminated class of priors;

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  1. Berger, J. & Berliner, L.M., 1984. "Bayesian input in Stein estimation and a new minimax empirical Bayes estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 25(1-2), pages 87-108.
  2. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wass, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 3(1), pages 5-124, June.
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