Optimal Dynamic Sample Allocation Among Strata

A dynamic sampling plan among strata is a permutation of sampled items specifying which stratum is to receive the next item to be included in the sample. An optimal such plan has the property of achieving minimum variance for its cost whenever it is truncated. This article shows that optimal dynamic sampling plans exist under very general conditions, and gives a simple algorithm for constructing them. The well-known Neyman allocation is compared to the dynamic optimum, both statically and dynamically. The theorems rely on a version of the Neyman-Pearson Lemma adapted for use in search theory.