Summary
Fix a family C of continuous distributions on the line. Sufficient and (different) necessary conditions on C are given in order that the sample distribution function be an optimal estimator in the asymptotic minimax sense. The abstract results are illustrated by a variety of concrete families C that have arisen in the literature; some of these illustrations settle known, but previously unsolved, problems. Methods involve systematic consideration of statistical experiments whose parameter lies in a Hilbert space, and the theory of abstract Wiener spaces.
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Millar, P.W. Asymptotic minimax theorems for the sample distribution function. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 233–252 (1979). https://doi.org/10.1007/BF00537522
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DOI: https://doi.org/10.1007/BF00537522