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Asymptotics in Bayesian decision theory with applications to global robustness

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  • Abraham, Christophe

Abstract

We provide the rate of convergence of the Bayes action derived from non smooth loss functions involved in Bayesian robustness. Such loss functions are typically not twice differentiable but admit right and left second derivatives. The asymptotic limit of three measures of global robustness is given. These measures are the range of the Bayes actions set associated with 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 ranges over a given class. An application to prior robustness with density ratio classes is provided.

Suggested Citation

  • Abraham, Christophe, 2005. "Asymptotics in Bayesian decision theory with applications to global robustness," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 50-65, July.
  • Handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:50-65
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    References listed on IDEAS

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    1. Christophe Abraham & Jean-Pierre Daurès, 1999. "Analytic approximation of the interval of Bayes actions derived from a class of loss functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 129-145, June.
    2. Strasser, Helmut, 1975. "The asymptotic equivalence of Bayes and maximum likelihood estimation," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 206-226, June.
    3. Abraham, Christophe, 2001. "Asymptotic Limit of the Bayes Actions Set Derived from a Class of Loss Functions," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 251-274, November.
    4. Chris M Theobald & Mike Talbot, 2002. "The Bayesian choice of crop variety and fertilizer dose," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(1), pages 23-36.
    5. Strasser, Helmut, 1973. "On Bayes estimates," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 293-310, September.
    6. Christophe Abraham & Jean-Pierre Daures, 2000. "Global Robustness with Respect to the Loss Function and the Prior," Theory and Decision, Springer, vol. 48(4), pages 359-381, June.
    7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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