A sharp boundary for SURE-based admissibility for the normal means problem under unknown scale

Yuzo Maruyama, William E. Strawderman

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1 Scopus citations

Abstract

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined in terms of non-existence/existence of a solution to a differential inequality based on Stein's unbiased risk estimate (SURE). We find a sharp boundary between quasi-admissible and quasi-inadmissible estimators related to the optimal James–Stein estimator. We also find a class of priors related to the Strawderman class in the known variance case where the boundary between quasi-admissibility and quasi-inadmissibility corresponds to the boundary between admissibility and inadmissibility in the known variance case. Additionally, we also briefly consider generalization to the case of general spherically symmetric distributions with a residual vector.

Original languageEnglish (US)
Pages (from-to)134-151
Number of pages18
JournalJournal of Multivariate Analysis
Volume162
DOIs
StatePublished - Nov 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Keywords

  • Admissibility
  • Generalized Bayes
  • Stein's unbiased risk estimate

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