On -Minimax Estimation with Ordered Observations
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[In this note we derive -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, . We restrict ourselves to the rules which are linear combinations of order statistics. Optimal decision rules in such decision-theoretic framework are, as expected, rules linear in the minimal sufficient statistics, X and $(X_{1colon n},X_{ncolon n})$. However in the "no intercept" - class of decision rules, the optimal -minimax rule requires knowledge of all order statistics.]
