Statistical Papers

, Volume 29, Issue 1, pp 45–57 | Cite as

Two point priors and Γ-minimax estimating in families of uniform distributions

  • Laxiang Chen
  • Jürgen Eichenauer


It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.

AMS 1980 subject classifications

Primary: 62 C 99 Secondary: 62 F 10 

Key words and phrases

Gamma-minimax uniform distribution squared error loss least favourable two point prior 


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Laxiang Chen
    • 1
  • Jürgen Eichenauer
    • 1
  1. 1.Fachbereich Mathematik, Arbeitsgruppe Stochastik und Operations ResearchTechnische Hochschule DarmstadtDarmstadt

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