EMAP Statistical Methods Manual
DRAFT (To be submitted to Environmetrics)
Variance Estimation for Spatially Balanced Samples of Environmental
Don L. Stevens, Jr.1 and Anthony R. Olsen2
1 Dynamac Corporation, Corvallis, OR
2 US EPA ORD, NHEERL WED, 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