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

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Abstract

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.

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Chen, L., Eichenauer, J. Two point priors and Γ-minimax estimating in families of uniform distributions. Statistical Papers 29, 45–57 (1988). https://doi.org/10.1007/BF02924510

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  • DOI: https://doi.org/10.1007/BF02924510

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