Center Sampling: a strategy for elusive population surveys

Center sampling is useful in finite population surveys when exhaustive lists of all units are not available and the target population is naturally clustered into a number of overlapping sites spread over an area of interest such as, for instance, the immigrant population illegally resident in a country. Center sampling has been successfully employed in official European surveys; nevertheless few systematic theoretical results have been given yet to support empirical findings. In this paper a general theory for Center sampling is formalized and an unbiased estimator for the mean of a quantitative or dichotomous characteristic is proposed together with its exact variance. A suitable estimator for the variance, unbiased under simple random sampling, is also derived and the optimum allocation of the sample size among centers subject to linear cost constraints is discussed. Other sampling designs, useful under operational aspects, are also considered.