Optimality of the recursive Neyman allocation

TL;DR

This paper provides a formal proof of the optimality of the recursive Neyman allocation method for stratified sampling, introduces a new proof approach, and compares algorithm efficiencies with ready-to-use R implementations.

Contribution

It introduces a V-allocation framework to prove the optimality of the recursive Neyman algorithm and related methods, offering a unified and efficient proof approach.

Findings

Proof of the optimality of recursive Neyman allocation (rNa).

Comparison of running times for rNa, SGa, and coma algorithms.

Availability of R implementations for practical use.

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.