Spatially Balanced Sampling of Continuous Populations

When sampling from a continuous population (or distribution), we often want a rather small sample due to some cost attached to processing the sample or to collecting information in the field. Moreover, a probability sample that allows for design-based statistical inference is often desired. Given these requirements, we want to reduce the sampling variance of the Horvitz-Thompson estimator as much as possible. To achieve this, we introduce different approaches to using the local pivotal method for selecting well-spread samples from multidimensional continuous populations. The results of a simulation study clearly indicate that we succeed in selecting spatially balanced samples and improve the efficiency of the Horvitz-Thompson estimator.