A large number of sampling algorithms with unequal probabilities have been proposed in the literature, see for example Tillé (2011) for a review. The choice of a sampling algorithm is based on both statistical ans practical considerations. In this work, we consider the use of the pivotal method (Deville and Tillé, 1998).

It is based on a principle of duels between units, and leads to a variance reduction if the order of the units in the population is informative. This is a sequential method, so that it can be particularly helpful when sampling in a dataflow. Also, it enables to avoid selecting neighboring units, which makes it useful in the context of spatial sampling, when we wish to select spatially balanced samples.

In this talk, we will describe the principles of the method, and prove that it guarantees good statistical properties for a Horvitz-Thompson estimator (weak consistency, central limit-theorem, exponential inequality). We will present an  application of the method as a modification of the Generalized Random Tesselation Stratified (GRTS) sampling method, which is commonly used in spatial sampling. This is joint work with Ronan le Gleut.