estimation of a normal mean matrix

A few days ago, I noticed the paper Estimation under matrix quadratic loss and matrix superharmonicity by Takeru Matsuda and my friend Bill Strawderman had appeared in Biometrika. (Disclaimer: I was not involved in handling the submission!) This is a “classical” shrinkage estimation problem in that covariance matrix estimators are compared under under a quadratic loss, using Charles Stein’s technique of unbiased estimation of the risk is derived. The authors show that the Efron–Morris estimator is minimax. They also introduce superharmonicity for matrix-variate functions towards showing that generalized Bayes estimator with respect to a matrix superharmonic priors are minimax., including a generalization of Stein’s prior. Superharmonicity that relates to (much) earlier results by Ed George (1986), Mary-Ellen Bock (1988),  Dominique Fourdrinier, Bill Strawderman, and Marty Wells (1998). (All of whom I worked with in the 1980’s and 1990’s! in Rouen, Purdue, and Cornell). This paper also made me realise Dominique, Bill, and Marty had published a Springer book on Shrinkage estimators a few years ago and that I had missed it..!

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