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Spatially balanced sampling
[2018 KAIST Math. Colloquium]
Date: 2018-10-04
Speaker : Yves Tillé (Institute of Statistics, University of Neuchatel)
Abstract : Spatial sampling is particularly important for environmental statistics. A simple reasoning developed in Grafström and Tillé (2013) shows that under a self-correlated linear model, it is more efficient to select a well-spread sample in space. If we select two neighbouring units in a sample, we will tend to collect partially redundant information. Grafström and Lundström (2013) discuss at length the concept of spreading, also known as spatial balancing and its implication on estimation. The Generalized Random Tesselation Sampling GRTS design has been proposed by Stevens Jr. and Olsen (1999, 2004, 2003) to select spread samples. The pivotal method has been proposed by Deville and Tillé (2000). Grafström et al. (2012) proposed to use the pivotal method for spatial sampling. This method, called the local pivotal method, consists, at each step, in comparing two neighboring units. If the probability of one of these two units is increased, the probability of the other is decreased, which induces a repulsion between the units. The natural extension of this idea is to confront a group of units. The local pivot method was generalized by Grafström and Tillé (2013) to provide samples that are both well-balanced in space and balanced on the totals of the auxiliary variables. This method is called the local cube method. We also propose a new method that enables us to select spreader samples that all existing methods and allows the construction of periodic sampling plans when these plans exist.
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