Asymptotic properties of the sample mean in adaptive sequential sampling with multiple selection criteria

‎We extend the method of adaptive two-stage sequential sampling to‎ ‎include designs where there is more than one criteria is used in‎ ‎deciding on the allocation of additional sampling effort‎. ‎These‎ ‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎ ‎population‎, ‎or a measure of some related population‎. ‎We develop‎ ‎Murthy estimator for the design that is unbiased estimators for‎ ‎the population mean‎, ‎and propose another‎, ‎more efficient‎, ‎estimator‎. ‎We investigate asymptotic properties of this estimator‎.‎We use a simulation study to investigate design properties of the‎ ‎multi-criteria adaptive sequential sampling scheme and also some‎ ‎estimator properties under the design‎.