Journal Article

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

A. Boisbunon and Y. Maruyama

in Biometrika

Published on behalf of The Biometrika Trust

Volume 101, issue 3, pages 733-740
Published in print September 2014 | ISSN: 0006-3444
Published online July 2014 | e-ISSN: 1464-3510 | DOI:

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This work treats the problem of estimating the predictive density of a random vector when both the mean vector and the variance are unknown. We prove that the density of reference in this context is inadmissible under the Kullback–Leibler loss in a nonasymptotic framework. Our result holds even when the dimension of the vector is strictly lower than three, which is surprising compared to the known variance setting. Finally, we discuss the relationship between the prediction and the estimation problems.

Keywords: Bayes rule; Inadmissibility; Multivariate normal distribution; Prior distribution; Unknown variance

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Subjects: Biomathematics and Statistics ; Probability and Statistics