Bayesian predictive densities based on superharmonic priors for the 2-dimensional Wishart model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Komaki, Fumiyasu^1,2 

[1] Univ Tokyo, Dept Math Informat, Grad Sch Informat Sci & Technol, Bunkyo Ku, Tokyo 1138656, Japan

[2] RIKEN, Brain Sci Inst, Wako, Saitama 3510198, Japan

关键词: Differential geometry;    Green's theorem;    Group models;    Jeffreys prior;    Kullback-Leibler divergence;    Minimaxity;    Orthogonally invariant priors;    Right invariant prior;   

DOI  :  10.1016/j.jmva.2009.04.014

来源: Elsevier

【 摘 要 】

Bayesian predictive densities for the 2-dimensional Wishart model are investigated. The performance of predictive densities is evaluated by using the Kullback-Leibler divergence. It is proved that a Bayesian predictive density based on a prior exactly dominates that based on the Jeffreys prior if the prior density satisfies some geometric conditions. An orthogonally invariant prior is introduced and it is shown that the Bayesian predictive density based on the prior is minimax and dominates that based on the right invariant prior with respect to the triangular group. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free