Affordable Access

deepdyve-link
Publisher Website

Stein Estimation for Spherically Symmetric Distributions: Recent Developments

Authors
Type
Published Article
Publication Date
Submission Date
Identifiers
DOI: 10.1214/10-STS323
Source
arXiv
License
Yellow
External links

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.

Statistics

Seen <100 times