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On Consistency of the Bayes Estimator of the Density

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  • Agustín G. Nogales

    (Departamento de Matemáticas, IMUEx, Universidad de Extremadura, 06006 Badajoz, Spain)

Abstract

Under mild conditions, strong consistency of the Bayes estimator of the density is proved. Moreover, the Bayes risk (for some common loss functions) of the Bayes estimator of the density (i.e., the posterior predictive density) goes to zero as the sample size goes to ∞. In passing, a similar result is obtained for the estimation of the sampling distribution.

Suggested Citation

  • Agustín G. Nogales, 2022. "On Consistency of the Bayes Estimator of the Density," Mathematics, MDPI, vol. 10(4), pages 1-6, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:636-:d:753072
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    References listed on IDEAS

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    1. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, October.
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    Cited by:

    1. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

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