Optimizing a mixed allocation

This article proposes a criterion for calculating the trade-off in so-called “mixed” allocations, which combine two classic allocations in sampling theory. In INSEE (National Institute of Statistics and Economic Studies) business surveys, it is common to use the arithmetic mean of a proportional allocation and a Neyman allocation (corresponding to a trade-off of 0.5). It is possible to obtain a trade-off value resulting in better properties for the estimators. This value belongs to a region that is obtained by solving an optimization program. Different methods for calculating the trade-off will be presented. An application for business surveys is presented, as well as a comparison with other usual trade-off allocations.