On Admissibility in Bipartite Incidence Graph Sampling

Abstract In bipartite incidence graph sampling, the target study units may be formed as connected population elements, which are distinct from the units of sampling, and there may exist generally more than one way by which a given study unit can be observed via sampling units. This generalizes finite-population element or multistage sampling, where each element can only be sampled directly or via a single primary sampling unit. We study the admissibility of estimators in bipartite incidence graph sampling, where a minimal level of knowledge is available of the connections between the sampling and study units to enable design-unbiased estimation. We prove that there exist many other admissible estimators than the classic Horvitz–Thompson estimator. Our result also fills a gap in the literature of unconventional finite-population sampling, where other unbiased estimators provide alternatives to the Horvitz–Thompson estimator.