Statistical Science

Stein Estimation for Spherically Symmetric Distributions: Recent Developments

Ann Cohen Brandwein and William E. Strawderman

Full-text: Open access

Abstract

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.

Article information

Source
Statist. Sci., Volume 27, Number 1 (2012), 11-23.

Dates
First available in Project Euclid: 14 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.ss/1331729979

Digital Object Identifier
doi:10.1214/10-STS323

Mathematical Reviews number (MathSciNet)
MR2953492

Zentralblatt MATH identifier
1330.62285

Keywords
Stein estimation spherical symmetry minimaxity admissibility

Citation

Brandwein, Ann Cohen; Strawderman, William E. Stein Estimation for Spherically Symmetric Distributions: Recent Developments. Statist. Sci. 27 (2012), no. 1, 11--23. doi:10.1214/10-STS323. https://projecteuclid.org/euclid.ss/1331729979


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