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EMAP Statistical Methods Manual

DRAFT  (To be submitted to Environmetrics)

Variance Estimation for Spatially Balanced Samples of Environmental Resources

Don L. Stevens, Jr.1 and Anthony R. Olsen2

1 Dynamac Corporation, Corvallis, OR



The spatial distribution of a natural resource is an important consideration in designing an 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 paper, 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.

Keywords: spatial sampling, Horvitz-Thompson, environmental monitoring



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