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February 2012 Stein Estimation for Spherically Symmetric Distributions: Recent Developments
Ann Cohen Brandwein, William E. Strawderman
Statist. Sci. 27(1): 11-23 (February 2012). DOI: 10.1214/10-STS323


This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not. Considerable attention is devoted to generalizing the “Stein lemma” which underlies much of the theoretical development of improved minimax estimation for spherically symmetric distributions. A main focus is on distributional robustness results in cases where a residual vector is available to estimate an unknown scale parameter, and, in particular, in finding estimators which are simultaneously generalized Bayes and minimax over large classes of spherically symmetric distributions. Some attention is also given to the problem of estimating a location vector restricted to lie in a polyhedral cone.


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Ann Cohen Brandwein. William E. Strawderman. "Stein Estimation for Spherically Symmetric Distributions: Recent Developments." Statist. Sci. 27 (1) 11 - 23, February 2012.


Published: February 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1330.62285
MathSciNet: MR2953492
Digital Object Identifier: 10.1214/10-STS323

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.27 • No. 1 • February 2012
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