On the estimation of a normal variance

Sándor Csörgö, Julian J. Faraway

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


Complementing Rukhin's [5] investigations, the mean squared error of members of a family of preliminary-test estimators and members of the basic family of shrinkage estimators are compared. The reference point is Stein's [10] estimator that is contained in both classes. It turns out that Stein's estimator has certain qualitative optimality properties among the preliminary-test estimators. But it also turns out that, while Rukhin's 4% maxim in the minimax shrinkage class is well known and frequently cited, without minimaxity greater improvements can be achieved in his local sense by estimators coming from the preliminary-test class. This underlines another aspect of Stein's original insight. Most of our findings are presented graphically.

Original languageEnglish
Pages (from-to)23-34
Number of pages12
JournalStatistics and Risk Modeling
Issue number1
Publication statusPublished - 1 Jan 1996


  • preliminary-test and shrinkage estimators
  • quadratiç risk

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty


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