On the estimation of a restricted normal mean

Constantine Gatsonis, Brenda MacGibbon, William Strawderman

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19 Scopus citations


Let X ∼ N(θ,1), where θ ε{lunate} [-m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [-m, m], dominates δ0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

Original languageEnglish (US)
Pages (from-to)21-30
Number of pages10
JournalStatistics and Probability Letters
Issue number1
StatePublished - Sep 1987

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • bounded normal mean
  • minimax
  • uniform prior

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