Adaptive cluster double sampling

We present a multi-phase variant of adaptive cluster sampling which allows the sampler to control the number of measurements of the variable of interest. A first-phase sample is selected using an adaptive cluster sampling design based on an inexpensive auxiliary variable associated with the survey variable. Then the network structure of the adaptive cluster sample is used to select an ordinary one-phase or two-phase subsample of units and the values of the survey variable associated with those units are recorded. The population mean is estimated by either a regression-type estimator or a Horvitz-Thompson-type estimator. The results of a simulation study show good performance of the proposed design, and suggest that in many real situations this design might be preferred to the ordinary adaptive cluster sampling design.