Adaptive cluster sampling with networks selected without replacement

In the adaptive cluster design introduced by Thompson (1990), a finite population of units under investigation is partitioned into networks on the basis of a specified condition for adding neighbourhoods to a sampled unit. An initial sample of units is taken and a network may be sampled more than once. In this paper, we introduce a-modification of the design in which networks are sampled only once. Two unbiased estimators are considered and the Rao-Blackwell theorem is used to improve them in terms of efficiency. The various estimators are compared using two examples.