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Abstract:
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Optimal sample allocation can improve the precision of estimates for surveys with fixed budgets. Demographic surveys at the Census Bureau often have precision requirements for estimates at both the national- and sub-national-level. This results in a hierarchical relationship between the national- and sub-national precision requirements. For example, for a fixed budget, sample is allocated such that the sub-national requirements are met then the balance of the remaining sample is allocated such that the national-level requirement is satisfied. The focus of this paper is to explore optimization techniques that satisfy this hierarchical sample allocation problem. Using the Current Population Survey, this research compares four methods for allocating sample units that simultaneously meet the state- and national-level requirements. The four methods considered are non-linear optimization, a linear programming algorithm, a maximum sampling interval step reduction, and a greedy heuristic. The results show that all of the methods are capable of satisfying the design requirements with the greedy heuristic resulting in the most efficient allocation for meeting the national-level precision requirement. However, the nonlinear optimization can provide a less greedy sample allocation across states.
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