Stein estimation: The spherically symmetric case

Ann Cohen Brandwein, William E. Strawderman

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This paper presents an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; b) that the amount of shrinkage allowable to preserve domination over the best invariant estimator is, when properly interpreted, relatively free from the assumption of normality; and c) that the potential savings in risk are substantial when accompanied by good quality prior information.

Original languageEnglish (US)
Pages (from-to)356-369
Number of pages14
JournalStatistical Science
Issue number3
StatePublished - Aug 1990

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Concave loss
  • Decision theory
  • Minimaxity
  • Quadratic loss
  • Spherical symmetry
  • Stein estimation


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