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

• 成果类型: Article
• 署名作者: Boisbunon, A.; Maruyama, Y.
• 署名单位: University of Tokyo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu024
• 发表日期: 2014
• 页码: 733740
• 关键词: bayesian prediction; shrinkage priors

摘要

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.