A correlation-shrinkage prior for Bayesian prediction of the two-dimensional Wishart model

Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage

T Sei and F Komaki

Biometrika, 2022, vol. 109, issue 4, 1173-1180

Abstract: SummaryA 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 -transformation of the correlation coefficient. The Bayesian predictive density based on the prior is shown to be minimax.

Keywords: Decision theory; Gauss hypergeometric function; Minimaxity; Right invariant prior; Scale invariance; Superharmonic prior (search for similar items in EconPapers)
Date: 2022
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