Risk-efficient nonparametric sequential estimators
type: Item
instance of: scholarly article
title: Risk-efficient nonparametric sequential estimators
zbMATH Open document ID: 0609.62121
DOI: 10.1007/BF02613127
author: W. Goldmann
published in: Metrika
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176092
review text: Let \(x_ 1,x_ 2,x_ 3,..\). be a sequence of independent identically distributed random variables and \(\tau\) an estimable parameter of their distribution. We want to estimate \(\tau\) by the corresponding U-statistic \(u_ n\) with loss function \((u_ n-\tau)^ 2+cn\). We derive a stopping time and prove its risk-efficiency in the sense of \textit{N. Starr} [Ann. Math. Stat. 37, 1173-1185 (1966; Zbl 0144.408)] without any assumption on the nature of the distribution function other than the existence of some moments.
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 3986474
zbMATH Keywords: sample-size efficiency
zbMATH Keywords: U-statistic
zbMATH Keywords: loss function
zbMATH Keywords: stopping time
zbMATH Keywords: risk- efficiency
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3986474