Stratified sampling has been commonly used in many large-scale surveys. The two inter-related problems of determining strata boundaries where strata have to be developed using some variable(s) whose values can be accessed while designing the survey and of allocating the total sample size among the strata have been studied during a long period, initially without involving mathematical programming and subsequently using concurrent developments in constrained optimization methods and algorithms. The present article provides a critique of some of these studies, especially those dealing with multiple stratification variables and multiple parameters to be estimated.
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