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The simultaneous comparison of estimators. (English) Zbl 0860.62024
Summary: The definition of Pitman’s measure of closeness is generalized in order to simultaneously compare any finite number of estimators of a real parameter $$\theta$$. This generalization allows for the comparison of the worst estimator of one subset of the estimators with the best estimator of the remaining estimators under consideration. Many computational results, such as the Geary-Rao theorem and Karlin’s corollary, are generalized to compare more than two estimators. These generalizations are accomplished using methods in stochastic geometry.

##### MSC:
 62F10 Point estimation 60D05 Geometric probability and stochastic geometry