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April, 1969 The Consistency of Certain Sequential Estimators
R. M. Loynes
Ann. Math. Statist. 40(2): 568-574 (April, 1969). DOI: 10.1214/aoms/1177697724


The results described here have their roots in two areas, for in a certain sense we combine on the one hand the work of Girshick, Mosteller and Savage [5] and Wolfowitz [11] and [12] on sequential estimation of the binomial parameter, and on the other the result of Hoeffding [7] concerning the consistency of $U$-statistics. The link between the two is the Blackwell [2] procedure for obtaining another (better) estimator from a given one by taking expectations conditional on a sufficient statistic. The main result is that if from a given estimator $T$ of $\theta = ET$ we construct new estimators by the Blackwell procedure corresponding to a sequence of stopping-rules $N_i$, then this sequence of estimators is consistent provided $N_i$ tends to infinity in probability; in fact it has also to be assumed that the $N_i$ have a certain structural property.


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R. M. Loynes. "The Consistency of Certain Sequential Estimators." Ann. Math. Statist. 40 (2) 568 - 574, April, 1969.


Published: April, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0205.46504
MathSciNet: MR239692
Digital Object Identifier: 10.1214/aoms/1177697724

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 2 • April, 1969
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