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Risk-efficient nonparametric sequential estimators

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Summary

Letx 1,x 2,x 3, ... be a sequence of independent identically distributed random variables andτ an estimable parameter of their distribution. We want to estimateτ by the correspondingU-statisticu n with loss function (u n −τ)2 +cn. We derive a stopping time and prove its risk-efficiency in the sense of Starr (1966) without any assumption on the nature of the distribution function other than the existence of some moments.

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Authors and Affiliations

  1. Abteilung für Wahrscheinlichkeitstheorie und Mathematische Statistik, Universität Bonn, Institut für Angewandte Mathematik, Wegelerstraße 6, D 5300, Bonn 1, FRG

    Werner Goldmann

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  1. Werner Goldmann
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Research supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72, at the Universität Bonn.

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Goldmann, W. Risk-efficient nonparametric sequential estimators. Metrika 34, 25–30 (1987). https://doi.org/10.1007/BF02613127

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  • DOI: https://doi.org/10.1007/BF02613127

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