Inference under pivotal sampling: Properties,variance estimation,and application to tesselation for spatial sampling

Unequal probability sampling is commonly used for sample selection. In the context of spatial sampling, the variables of interest often present a positive spatial correlation, so that it is intuitively relevant to select spatially balanced samples. In this article, we study the properties of pivotal sampling and propose an application to tesselation for spatial sampling. We also propose a simple conservative variance estimator. We show that the proposed sampling design is spatially well balanced, with good statistical properties and is computationally very efficient.