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On Bayesian estimation of densities and sampling distributions: The posterior predictive distribution as the Bayes estimator

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  • Agustín G. Nogales

Abstract

Optimality results for three interesting Bayesian estimation problems are presented in this paper: the estimation of the sampling distribution for the squared total variation function, the estimation of the density for the L1‐squared loss function and the estimation of a real distribution function for the L∞‐squared loss function. The posterior predictive distribution provides the solution to these problems. Some examples are presented to illustrate it.

Suggested Citation

  • Agustín G. Nogales, 2022. "On Bayesian estimation of densities and sampling distributions: The posterior predictive distribution as the Bayes estimator," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 236-250, May.
    • Handle: RePEc:bla:stanee:v:76:y:2022:i:2:p:236-250
    DOI: 10.1111/stan.12258
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    1. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, November.
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    1. Agustín G. Nogales, 2022. "Optimal Bayesian Estimation of a Regression Curve, a Conditional Density, and a Conditional Distribution," Mathematics, MDPI, vol. 10(8), pages 1-22, April.

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