Affiliation:
1. Graduate School of Information Science and Technology, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan
Abstract
Summary
A Bayesian prediction problem for the two-dimensional Wishart model is investigated within the framework of decision theory. The loss function is the Kullback–Leibler divergence. We construct a scale-invariant and permutation-invariant prior distribution that shrinks the correlation coefficient. The prior is the geometric mean of the right invariant prior with respect to permutation of the indices, and is characterized by a uniform distribution for Fisher’s $z$-transformation of the correlation coefficient. The Bayesian predictive density based on the prior is shown to be minimax.
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability
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