A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non-adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non-adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.