Why Well Spread Probability Samples Are Balanced

Anton Grafström, Niklas L. P. Lundström

Department of Forest Resource Management, Swedish University of Agricultural Sciences, Ume?, Sweden.
Department of Mathematics and Mathematical Statistics, Ume? University, Ume?, Sweden.

DOI: 10.4236/ojs.2013.31005                

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.

Keywords

Balanced Sample; Local Pivotal Method; Spatial Balance; Spatially Correlated Poisson Sampling; Voronoi Polytopes

Conflicts of Interest

The authors declare no conflicts of interest.

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