Title
An Old Man's View of Multivariate Estimation
Speaker
Mark Berliner, The Ohio State University
Abstract
In 1955 Charles Stein shocked the statistics community by proving that the traditional MLE estimator of a multivariate normal mean is inadmissible under quadratic loss in three or more dimensions. In 1960 James and Stein presented an estimator that beats the traditional one. Later, a view emerged that one must use prior information to make significant improvement over the traditional estimator. This suggests that the Bayesian view is highly relevant: I review Stein estimation from the empirical, hierarchical and robust Bayesian viewpoints. A class of procedures that combines James-Stein estimators is discussed. The motivation for this talk is the question of the role of Stein estimation in modern Big Data settings. I will close the presentation with some discussion on this issue.