**Sankhya:
The Indian Journal of Statistics**

2005, Volume 67, Pt. 3, 590--612

**Maximal and Minimal Sample
Co-ordination**

Alina Matei and Yves Till\'e, University of Neuch\^atel, Switzerland

SUMMARY. For sampling design over time we are interested in maximizing/minimizing the expected overlap between two or more samples drawn in different time points. For this it is necessary to compute the joint inclusion probability of two samples drawn in different time periods. A solution is given by using linear programming and more precisely by solving a transportation problem. This solution is not computationally fast. We are interested in identifying the conditions under which the objective function associated with an optimal solution of the transportation problem is equal to the bound given by maximizing/minimizing the expected overlap. Using these conditions we propose a new algorithm to optimize the co-ordination between two samples without using linear programming. Our algorithm is based on the Iterative Proportional Fitting (IPF) procedure. Theoretical complexity is substantially lower than for transportation problem approach, because more than five iterations of IPF procedure are not required in practice.

*AMS (1991) subject classification. *62D05.

*Key words and phrases. *Sample survey, sample co-ordination, IPF
procedure, transportation problem.