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Minimax and \(\Gamma\)-minimax estimation for the Poisson distribution under LINEX loss when the parameter space is restricted. (English) Zbl 0958.62007

Summary: This paper considers the problems of minimax and \(\Gamma\)-minimax estimation under the LINEX loss function when the parameter space is restricted. A general property of the risk of the Bayes estimator with respect to the two-point prior is presented. Minimax and \(\Gamma\)-minimax estimators of the parameter of the Poisson distribution are obtained when the parameter of interest is known to lie in a small parameter space.

MSC:

62C20 Minimax procedures in statistical decision theory
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