TITLE:
Why Well Spread Probability Samples Are Balanced
AUTHORS:
Anton Grafström, Niklas L. P. Lundström
KEYWORDS:
Balanced Sample; Local Pivotal Method; Spatial Balance; Spatially Correlated Poisson Sampling; Voronoi Polytopes
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.1,
February
20,
2013
ABSTRACT: When sampling from a finite population there is often
auxiliary information available on unit level. Such information can be used to
improve the estimation of the target parameter. We show that probability
samples that are well spread in the auxiliary space are balanced, or
approximately balanced, on the auxiliary variables. A consequence of this
balancing effect is that the Horvitz-Thompson estimator will be a very good
estimator for any target variable that can be well approximated by a Lipschitz
continuous function of the auxiliary variables. Hence we give a theoretical
motivation for use of well spread probability samples. Our conclusions imply
that well spread samples, combined with the Horvitz- Thompson estimator,
is a good strategy in a varsity of situations.