Improved unbiased estimators in adaptive cluster sampling

The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics-not necessarily minimal-are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.