A Tribute to Charles Stein

Abstract

In 1956, Charles Stein published an article that was to forever change the statistical approach to high-dimensional estimation. His stunning discovery that the usual estimator of the normal mean vector could be dominated in dimensions 3 and higher amazed many at the time, and became the catalyst for a vast and rich literature of substantial importance to statistical theory and practice. As a tribute to Charles Stein, this special issue on minimax shrinkage estimation is devoted to developments that ultimately arose from Stein's investigations into improving on the UMVUE of a multivariate normal mean vector. Of course, much of the early literature on the subject was due to Stein himself, including a key technical lemma commonly referred to as Stein's Lemma, which leads to an unbiased estimator of the risk of an almost arbitrary estimator of the mean vector.