A Note on Consistency of the Bayes Estimator of the Density

Abstract

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

arXiv admin note: text overlap with arXiv:2008.00683

References in corpus (1)

• On Bayesian Estimation of Densities and Sampling Distributions: the Posterior Predictive Distribution as the Bayes Estimator