A biobjective method for sample allocation in stratified sampling

E. Carrizosa, D. Romero Morales

The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this nonlinear integer biobjective problem. In the first phase, all supported Pareto-optimal solutions are described via a closed formula, which enables quick computation. Moreover, for the common case in which sampling costs are independent of the strata, all Pareto-optimal solutions are shown to be supported. For more general cost structures, the non-supported Pareto-optimal solutions are found by solving a parametric knapsack problem. The methods and results obtained in this paper are also extended to more general settings, such as estimation problems with missing values and various types of multi-response sampling.

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