Inadmissibility of the best equivariant predictive density in the unknown variance case

2013/08/13 by Aurélie Boisbunon, Boisbunon, Aurélie, Yuzo Maruyama +1
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1308.2765

openalex publication_date 2013/08/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this work, we are concerned with the estimation of the predictive density of a Gaussian random vector where both the mean and the variance are unknown. In such a context, we prove the inadmissibility of the best equivariant predictive density under the Kullback-Leibler risk in a nonasymptotic framework. Our result stands whatever the dimension d of the vector is, even when d<=2, which can be somewhat surprising compared to the known variance setting. We also propose a class of priors leading to a Bayesian predictive density that dominates the best equivariant one. Throughout the article, we give several elements that we believe are useful for establishing the parallel between the prediction and the estimation problems, as it was done in the known variance framework.

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