Spatiotemporal sampling with spatial spreading and rotation of units in time

Abstract

When the sampled population belongs to a metric space, the selection of neighboring units will imply often similarities in the collected data due to their geographical proximity. In order to estimate parameters such as means or totals, it is therefore more efficient to select samples that are well distributed in space. Often, the interest lies not only in estimating a parameter at one point in time, but rather in estimating it at several points and studying its evolution. Because of the temporal autocorrelation of successive values from the same unit, a system of temporal rotation of the units in the samples must be provided. In other words, this type of problem forces us to consider two types of autocorrelation: spatial and temporal. In this article, we propose two new spatiotemporal sampling methods for equal or unequal inclusion probabilities. Systematic sampling is used to promote a rotation of the selection of the same unit over time, and thus address temporal spread. Both methods select samples that are well distributed in space at each sampling time. They differ by the fact that these samples are of random size for the first one, while for the second one, more complex, their sizes are controlled. Thus, the first method is called spatiotemporal sampling with random sample sizes (SPAR) and the second, spatiotemporal sampling with fixed sample sizes (SPAF). Simulations show that our methods outperform and generalize existing methods.