Two-stage adaptive cluster sampling

Adaptive cluster sampling is a powerful method for parameter estimation when a population is highly clumped with clumps widely separated. Unfortunately, its use has been somewhat limited until now because of the lack of a suitable theory for using a pilot survey to design an experiment with a given efficiency or expected cost. A two-stage sampling procedure using an initial sample of primary units that fills this role is described. As adaptive cluster sampling amounts to sampling clusters of secondary units, two schemes are possible depending on whether the clusters are allowed to overlap primary unit boundaries or not. For each of these schemes there are two types of unbiased estimators available based, respectively, on modifications of the well-known Horvitz-Thompson and Hansen-Hurwitz estimators. Questions of cost and efficiency are discussed. A demonstration example is given.