Optimality of the Recursive Neyman Allocation

Abstract

Abstract We derive a formula for the optimal sample allocation in a general stratified scheme under upper bounds on the sample strata sizes. Such a general scheme includes SRSWOR within strata as a special case. The solution is given in terms of V-allocation with V being the set of take-all strata. We use V-allocation to give a formal proof of optimality of the popular recursive Neyman algorithm, rNa. We also propose a quick proof of optimality of the algorithm of Stenger and Gabler, SGa, as well as of our proposed modification, coma. Finally, we compare running times of rNa, SGa, and coma. Ready-to-use R-implementations of these algorithms are available on CRAN repository at https://cran.r-project.org/web/packages/stratallo.