Shrinkage Estimation and Superharmonicity

Abstract

In this paper, we review the theory of shrinkage estimation and superharmonicity. First, we introduce Steinʼs paradox on estimation of the normal mean vector and explain its relationship with superharmonicity. Next, we investigate the extension to matrices, in which the shrinkage of singular values plays a key role for exploiting low-rankness. Finally, we illustrate recent developments on shrinkage predictive densities, empirical Bayes marix completion and matrix superharmonicity.