Online Program

Maximal, minimal sample co-ordination and associated bounds

Keywords: Fréchet bounds, joint selection probability of two samples, linear programming.

Sample co-ordination maximizes or minimizes the overlap of two or more samples selected from overlapping populations. It can be applied to designs with simultaneous or sequential sample selection. The degree of co-ordination is measured by the expected sample overlap, which is limited by theoretical bounds (absolute upper and lower bounds). Two types of bounds can be defined: on unit level and on marginal sampling designs' level. We consider the bounds on unit level, which depend on unit inclusion probabilities. If the expected overlap equals the absolute upper bound, the sample co-ordination is maximal; if the expected overlap equals the absolute lower bound, the sample co-ordination is minimal. It is possible to construct optimal sampling designs for given unit inclusion probabilities to realize maximal or minimal co-ordination. This approach was developed by Matei and Skinner (2009) and uses a combination of the iterative proportional fitting algorithm and the linear programming implementation to controlled sampling method. We study here the performance of this method using a real scenario survey based on Swiss municipality data set. Despite the computing facilities available nowadays, the problem can be prohibitively large even for moderately large population and sample size. The method is useful to solve moderate-sized sample co-ordination problems.