Unbiased estimators of binomial N with bounded variance based on two-stage sampling - Hu, Jun (Sequential analysis, 2025)
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.