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Stein estimation for spherically symmetric distributions: recent developments. (English) Zbl 1330.62285
Summary: 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.

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
62F15 Bayesian inference
62H12 Estimation in multivariate analysis
62B05 Sufficient statistics and fields
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References:
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