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Asymptotic Efficiency of Point Estimators in Bayesian Predictive Inference

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  • Emanuele Dolera

    (Department of Mathematics, University of Pavia, Via Adolfo Ferrata 5, 27100 Pavia, Italy
    Collegio Carlo Alberto, Piazza V. Arbarello 8, 10134 Torino, Italy)

Abstract

The point estimation problems that emerge in Bayesian predictive inference are concerned with random quantities which depend on both observable and non-observable variables. Intuition suggests splitting such problems into two phases, the former relying on estimation of the random parameter of the model, the latter concerning estimation of the original quantity from the distinguished element of the statistical model obtained by plug-in of the estimated parameter in the place of the random parameter. This paper discusses both phases within a decision theoretic framework. As a main result, a non-standard loss function on the space of parameters, given in terms of a Wasserstein distance, is proposed to carry out the first phase. Finally, the asymptotic efficiency of the entire procedure is discussed.

Suggested Citation

  • Emanuele Dolera, 2022. "Asymptotic Efficiency of Point Estimators in Bayesian Predictive Inference," Mathematics, MDPI, vol. 10(7), pages 1-27, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1136-:d:785287
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    3. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian nonparametric inference for species variety with a two parameter Poisson-Dirichlet process prior," Carlo Alberto Notebooks 123, Collegio Carlo Alberto.
    4. Rajiv Sambasivan & Sourish Das & Sujit K. Sahu, 2020. "A Bayesian perspective of statistical machine learning for big data," Computational Statistics, Springer, vol. 35(3), pages 893-930, September.
    5. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "A new estimator of the discovery probability," DEM Working Papers Series 007, University of Pavia, Department of Economics and Management.
    6. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian non‐parametric inference for species variety with a two‐parameter Poisson–Dirichlet process prior," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 993-1008, November.
    7. Dolera, Emanuele & Mainini, Edoardo, 2020. "On uniform continuity of posterior distributions," Statistics & Probability Letters, Elsevier, vol. 157(C).
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    1. Emanuele Dolera, 2022. "Preface to the Special Issue on “Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini’s 75th Birthday”," Mathematics, MDPI, vol. 10(15), pages 1-4, July.

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