Summary
In this paper we consider two-stage sampling from a finite population, and associated estimators of the population total, in a general setting which includes most two-stage procedures in the literature. The main result gives general conditions for asymptotic normality of the estimators. The proof is based on a martingale central limit theorem. It is indicated how the result can be extended to multi-stage procedures.
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Ohlsson, E. Asymptotic normality for two-stage sampling from a finite population. Probab. Th. Rel. Fields 81, 341–352 (1989). https://doi.org/10.1007/BF00340058
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DOI: https://doi.org/10.1007/BF00340058