Optimal sample coordination using controlled selection

Sample coordination maximizes or minimizes the overlap of two or more samples selected from overlapping populations. It can be applied to designs with simultaneous or sequential selection of samples. We propose a method for sample coordination in the former case. We consider the case where units are to be selected with maximum overlap using two designs with given unit inclusion probabilities. The degree of coordination is measured by the expected sample overlap, which is bounded above by a theoretical bound, called the absolute upper bound, and which depends on the unit inclusion probabilities. If the expected overlap equals the absolute upper bound, the sample coordination is maximal. Most of the methods given in the literature consider fixed marginal sampling designs, but in many cases, the absolute upper bound is not achieved. We propose to construct optimal sampling designs for given unit inclusion probabilities in order to realize maximal coordination. Our method is based on some theoretical conditions on joint selection probability of two samples and on the controlled selection method with linear programming implementation. The method can also be applied to minimize the sample overlap.