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Asymptotic results on the frequentist mean squared error of generalized Bayes point predictors

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  • Chang, In Hong
  • Mukerjee, Rahul

Abstract

An asymptotic formula for the frequentist mean squared error (MSE) of generalized Bayes point predictors is worked out. This formula yields an explicit second-order admissibility result when the underlying parameter is scalar valued. We note that probability-matching priors, including Jeffreys' prior, may not always behave well with respect to the MSE of generalized Bayes point predictors. On the other hand, it is seen that priors that match the posterior and frequentist MSEs of such predictors can also keep the frequentist MSE small.

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  • Chang, In Hong & Mukerjee, Rahul, 2004. "Asymptotic results on the frequentist mean squared error of generalized Bayes point predictors," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 65-71, March.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:1:p:65-71
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    References listed on IDEAS

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    1. José Manuel Corcuera & Federica Giummolè, 1999. "A Generalized Bayes Rule for Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 265-279, June.
    2. J. Ghosh & Rahul Mukerjee, 1993. "Frequentist validity of highest posterior density regions in the multiparameter case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 293-302, June.
    3. J. Ghosh & Rahul Mukerjee, 1993. "Corrections to “Frequentist validity of highest posterior density regions in the multiparameter case”," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 602-602, September.
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