Singular value shrinkage priors for Bayesian prediction

• 成果类型: Article
• 署名作者: Matsuda, Takeru; Komaki, Fumiyasu
• 署名单位: University of Tokyo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv036
• 发表日期: 2015
• 页码: 843854
• 关键词: regression; matrix

摘要

We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on our priors are minimax and dominate those based on the uniform prior in finite samples. In particular, our priors work well when the true value of the parameter has low rank.