On Γ-minimax Estimation with Ordered Observations
نویسنده
چکیده
In this note we derive Γ-minimax estimators for the location parameter of the normal and uniform models. All distributions with uniformly bounded variances and means belonging to a fixed interval form a class of priors, Γ. We restrict ourselves to the rules which are linear combinations of order statistics. Optimal decision rules in such decisiontheoretic framework are, as expected, rules linear in the minimal sufficient statistics, X̄ and (X1:n, Xn:n). However in the “no intercept”class of decision rules, the optimal Γ-minimax rule requires knowledge of all order statistics.
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