Singular Value Shrinkage Priors for Bayesian Prediction

Abstract

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.

References in corpus (1)

• Improved minimax predictive densities under Kullback--Leibler loss

Cited by in corpus (6)

• Ridge-type Linear Shrinkage Estimation of the Matrix Mean of High-dimensional Normal Distribution
• Empirical Bayes Matrix Completion
• Proper Bayes and Minimax Predictive Densities for a Matrix-variate Normal Distribution
• Minimax Predictive Density for Sparse Count Data
• Nearly minimax empirical Bayesian prediction of independent Poisson observables
• Estimation under matrix quadratic loss and matrix superharmonicity