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August 2004 Asymptotic global robustness in bayesian decision theory
Christophe Abraham, Benoît Cadre
Ann. Statist. 32(4): 1341-1366 (August 2004). DOI: 10.1214/009053604000000562


In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of observations n. Three usual measures of posterior global robustness are considered: the (range of the) Bayes actions set derived from a class of loss functions, the maximum regret of using a particular loss when the subjective loss belongs to a given class and the range of the posterior expected loss when the loss function ranges over a class. We show that the rate of convergence of the first measure of robustness is $\sqrt{n}$ , while it is n for the other measures under reasonable assumptions on the class of loss functions. We begin with the study of two particular cases to illustrate our results.


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Christophe Abraham. Benoît Cadre. "Asymptotic global robustness in bayesian decision theory." Ann. Statist. 32 (4) 1341 - 1366, August 2004.


Published: August 2004
First available in Project Euclid: 4 August 2004

zbMATH: 1047.62006
MathSciNet: MR2089127
Digital Object Identifier: 10.1214/009053604000000562

Primary: 62C10 , 62F15

Keywords: asymptotic robustness , Bayesian decision theory , class of loss functions

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 4 • August 2004
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