Stevens, D.L. and A.R. Olsen. 2003. Variance estimation for spatially balanced samples of environmental resources. Environmetrics 14:593-610. WED-02-110
The spatial distribution of a natural resource is an important consideration in designing n efficient survey or monitoring program for the resource. We review a unified strategy for designing probability samples of discrete, finite resource populations, such as lakes within some geographical region; linear populations, such as a stream network in a drainage basin, and continuous, two-dimensional populations, such as forests. The strategy can be viewed as a generalization of spatial stratification. In this article, we develop a local neighborhood variance estimator based on that perspective, and examine its behavior via simulation. The simulations indicate that the local neighborhood estimator is unbiased and stable. The Horvitz-Thompson variance estimator based on assuming independent random sampling (IRS) may be two times the magnitude of the local neighborhood estimate. An example using data from a generalized random-tessellation stratified design on the Oahe Reservoir resulted in local variance estimates being 22 to 58 percent smaller than Horvitz-Thompson IRS variance estimates. Variables with stronger spatial patterns had greater reductions in variance, as expected.