A review of Brown 1971 (in)admissibility results under scale mixtures of Gaussian priors

Yuzo Maruyama, William E. Strawderman

Research output: Contribution to journalReview articlepeer-review


Brown's 1971 paper “Admissible estimators, recurrent diffusions and insoluble boundary value problems” is a landmark in the admissibility literature. It nearly completely settles the issue of admissibility/inadmissibility for estimating the mean of a multivariate normal distribution with identity covariance under sum of squared error loss. We revisit this wonderful tour de force on its 50th anniversary and present an alternative and more direct proof of the result for generalized Bayes estimators corresponding to priors which are a subclass of scale mixtures of spherical normals.

Original languageEnglish (US)
Pages (from-to)78-93
Number of pages16
JournalJournal of Statistical Planning and Inference
StatePublished - Jan 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Admissibility
  • Bayes


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