Unbiased estimators of binomial N with bounded variance based on two-stage sampling

In many statistical estimation problems, it is impossible to bound the variance of an unbiased estimator for a parameter based on one single fixed-size sample, especially when some unknown nuisance parameter exists. This paper introduces Birnbaum-Healy-type two-stage sampling procedures for construc...

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Bibliographic Details
Published inSequential analysis Vol. 44; no. 3; pp. 366 - 375
Main Author Hu, Jun
Format Journal Article
LanguageEnglish
Published Taylor & Francis 03.07.2025
Subjects
Bounded variance
Monte Carlo simulations
two-stage sampling
unbiased estimation
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Summary:In many statistical estimation problems, it is impossible to bound the variance of an unbiased estimator for a parameter based on one single fixed-size sample, especially when some unknown nuisance parameter exists. This paper introduces Birnbaum-Healy-type two-stage sampling procedures for constructing guaranteed bounded variance unbiased estimators (BVUEs) of the binomial parameter N under both known and unknown success probability p. We establish the unbiasedness and bounded variance properties of the proposed estimators, and validate their performance via extensive sets of Monte Carlo simulations.
ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2025.2508231