Asymptotic Efficiency of Point Estimators in Bayesian Predictive Inference

Emanuele Dolera
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Emanuele Dolera: Department of Mathematics, University of Pavia, Via Adolfo Ferrata 5, 27100 Pavia, Italy

Mathematics, 2022, vol. 10, issue 7, 1-27

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.

Keywords: asymptotic efficiency; bayesian predictive inference; compatibility equations; decision theory; de Finetti’s representation theorem; exchangeability; Wasserstein distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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