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Asymptotics in Bayesian decision theory with applications to global robustness

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  • Abraham, Christophe
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 95 (2005)
    Issue (Month): 1 (July)
    Pages: 50-65

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    Handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:50-65

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    Related research

    Keywords: Bayesian robustness Class of loss functions Class of priors Asymptotic rate of convergence Misspecified models;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
    2. Christophe Abraham & Jean-Pierre Daures, 2000. "Global Robustness with Respect to the Loss Function and the Prior," Theory and Decision, Springer, Springer, vol. 48(4), pages 359-381, June.
    3. Abraham, Christophe, 2001. "Asymptotic Limit of the Bayes Actions Set Derived from a Class of Loss Functions," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 79(2), pages 251-274, November.
    4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    5. 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, Springer, vol. 8(1), pages 129-145, June.
    6. Strasser, Helmut, 1975. "The asymptotic equivalence of Bayes and maximum likelihood estimation," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 5(2), pages 206-226, June.
    7. 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.
    8. Strasser, Helmut, 1973. "On Bayes estimates," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 3(3), pages 293-310, September.
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