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

Autor:	T Sei, F Komaki
Rok vydání:	2022
Předmět:	Statistics and Probability Applied Mathematics General Mathematics Statistics Probability and Uncertainty General Agricultural and Biological Sciences Agricultural and Biological Sciences (miscellaneous)
Zdroj:	Biometrika. 109:1173-1180
ISSN:	1464-3510 0006-3444
DOI:	10.1093/biomet/asac006
Popis:	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.
Databáze:	OpenAIRE
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