Risk-efficient nonparametric sequential estimators |
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Authors: | Dr Werner Goldmann |
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Institution: | 1. Abteilung für Wahrscheinlichkeitstheorie und Mathematische Statistik, Universit?t Bonn, Institut für Angewandte Mathematik, Wegelerstra?e 6, D 5300, Bonn 1, FRG
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Abstract: | 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.
Research supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72, at the Universit?t Bonn. |
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Keywords: | |
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