Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix

Hisayuki Tsukuma and Tatsuya Kubokawa

Journal of Multivariate Analysis, 2017, vol. 159, issue C, 138-150

Abstract: This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage estimators of the normal mean matrix. The Kullback–Leibler loss is used for evaluating decision-theoretic optimality of predictive densities. It is shown that a proper hierarchical prior yields an admissible and minimax predictive density. Also, some minimax predictive densities are derived from superharmonicity of prior densities.

Keywords: Admissibility; Gauss’ divergence theorem; Generalized Bayes estimator; Inadmissibility; Kullback–Leibler loss; Minimaxity; Shrinkage estimator; Statistical decision theory (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2017.05.004

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