Maximizing the conditional overlap in business surveys

This article presents novel sequential methods of sample coordination appropriate for a repeated survey, with a stratified design and simple random sampling without replacement (SRSWOR) selection within each stratum, when the composition or definition of strata changes. Such changes could be the result of updating the frame for births, deaths, or the modification of the industry classification system. Given that a sample has already been selected according to a first (before the frame updates) SRSWOR design, our general aim is to select a minimum number of new units for the second (after the updates) survey while preserving the first-order inclusion probabilities of units in the second SRSWOR design. Sequential methods presently in use can attain a large expected overlap, but do not control the overlap on each pair of selected samples. In this article we present a set of new methods for maximizing the expected overlap, which can handle realistic situations when strata and the associated sample sizes are large. These methods include one that not only maximizes the expected overlap but, for any initially selected sample, maximizes its overlap with the second sample; its superior performance is illustrated with numerical examples.