Optimality of the recursive Neyman allocation

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. This approach is convenient also for a quick proof of optimality of the algorithm of Stenger and Gabler (2005), SGa, as well as of its modification, coma, we propose here. 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.