A retrospective multi-period sampling approach

A number of applications, including claims made under Federal social welfare programs, audits conducted to verify corporate financial conditions, and audit inspections of critical medical products, require retrospective sampling over multiple time periods. A key characteristic of such samples may be that population members will appear in multiple time periods. When this occurs, and when the marginal cost of obtaining multiperiod information is minimum for a member appearing in the sample of the period being actually sampled, then a method which is herein called progressive random sampling (PRS) may be applied. Such a method, which uses information from early samples to reduce the sampling variability of later samples, thereby either improving sampling estimates for a given sample size or allowing effective reductions in sample sizes, is developed in this paper. As an illustration, an example application is included to demonstrate the PRS method