Simultaneous Optimization for Two Stage Area Sampling

A method for simultaneous optimization of all the parameters of a two-stage area sample design is proposed. In area sample surveys, estimates precision is influenced by the size of the area units. Often, for reducing travel costs, a two stage sample design is adopted. In these cases, the size of primary sampling units (PSUs) and secondary sampling units (SSUs) as well as the number of PSUs and SSUs to be selected can be chosen by the sampler. Carfagna (2000), under a fixed budget, computes the optimum SSU size for a single stage sampling, then determines the optimum set of size of PSU and number of PSUs and SSU to be selected. This procedure assumes that PSUs are much larger than SSUs, thus clustering SSUs within PSUs does not affect the optimum size of SSUs. Although this assumption is reasonable, in this paper, we explore the possibility of simultaneous optimization for the set of variables involved in the two stage area sample design.