A Tribute to Charles Stein
Statistical Science just ran a special issue (Feb. 2012) as a tribute to Charles Stein that focused on shrinkage estimation. Shrinkage and the Stein effect have been my entries to the Bayesian (wonderful) world, so I read through this series of papers edited by Ed George and Bill Strawderman with fond remembrance. The more because most of the authors are good friends! Jim Berger, Bill Jefferys, and Peter Müller consider shrinkage estimation for wavelet coefficients and applies it to Cepheid variable stars. The paper by Ann Brandwein and Bill Strawderman is a survey of shrinkage estimation and the Stein effect for spherically elliptical distributions, precisely my PhD thesis topic and main result! Larry Brown and Linda Shao give a geometric interpretation of the original Stein (1956) paper. Tony Cai discusses the concepts of minimaxity and shrinkage estimators in functional spaces. George Casella and Juinn Gene Hwang recall the impact of shrinkage estimation on confidence sets. Dominique Fourdrinier and Marty Wells give an expository development of loss estimation using shrinkage estimators. Ed George, Feng Liang and Xinyi Xu recall how shrinkage estimation was recently extended to prediction using Kullback-Leibler losses. Carl Morris and Martin Lysy detail the reversed shrinkage defect and Model-II minimaxity in the normal case. Gauri Datta and Malay Ghosh explain how shrinkage estimators are paramount in small area estimation, providing a synthesis between both the Bayesian and the frequentist points of view. At last, Michael Perlman and Sanjay Chaudhuri reflect on the reversed shrinkage effect, providing us with several pages of Star Trek dialogues on this issue, and more seriously voicing a valid Bayesian reservation!