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

• 成果类型: Article
• 署名作者: Sei, T.; Komaki, F.
• 署名单位: University of Tokyo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac006
• 发表日期: 2022
• 页码: 11731180
• 关键词: correlation-coefficient; Covariance matrices

摘要

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.