OPTIMAL SAMPLING DESIGNS FOR DEPENDENT SPATIAL UNITS

A geographical domain is partitioned into a set, with cardinality N, of areal units (i.e. census tracts), each of them having an attribute variable z. Observations are often to be recorded for a subset S of areal units whose cardinality is n. Under the hypothesis of dependence of the underlying data generating process Z, the following questions are considered: which is the best linear unbiased estimator (BLUE) of the mean of the process Z, and which is the subset S that minimizes the variance of this estimator? A weighted average estimator is used and the performances of some combinatorial optimization algorithms are tested to solve this problem. The simulated annealing algorithm is shown to be a suitable solution even when dealing with large data sets. Moreover, numerical comparisons are made between sampling designs obtained by using simulated annealing and the classical simple random and systematic sampling criteria.