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Displaying similar documents to “On the general minimax theorem”

Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function

Agata Boratyńska (2002)

Applicationes Mathematicae

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The problem of posterior regret Γ-minimax estimation under LINEX loss function is considered. A general form of posterior regret Γ-minimax estimators is presented and it is applied to a normal model with two classes of priors. A situation when the posterior regret Γ-minimax estimator, the most stable estimator and the conditional Γ-minimax estimator coincide is presented.

Two-point priors and minimax estimation of a bounded parameter under convex loss

Agata Boratyńska (2005)

Applicationes Mathematicae

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The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

Gamma-minimax estimators in the exponential family

Lanxiang Chen, Heike Hofmann, Jürgen Eichenauer-Herrmann, Jürgen Kindler

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The Γ-minimax estimator under squared error loss for the unknown parameter of a one-parameter exponential family with an unbiased sufficient statistic having a variance which is quadratic in the parameter is explicitly determined for a class Γ of priors consisting of all distributions whose first two moments are within some given bounds. This generalizes the choice of Γ in Jackson et al. (1970) as well as the unrestricted case. It is shown that the underlying statistical game is always...