Response designs and support regions in sampling continuous domains
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Stevens, D.L., Jr. and Urquhart, N.S. (1999)
Environmetrics, 11, 13-41.
Abstract
In many environmental samples, the target population is distributed over space
in a more or less continuous manner, e.g., the waters of lake or the trees in a
forest. Attributes of such a population can be conceptualized as a continuous
function defined on the spatial domain of the population. Some attributes
(e.g., water temperature) can be observed at a point; others (e.g., species
diversity) can only be determined over a finite extent or support region. A
fixed-shape support with uniform weights leads to an unbiased estimator of the
population total; however, it may be impossible to maintain a fixed shape near
domain boundaries. From a purely formal standpoint, unbiasedness can be
maintained by using differential weights or by changing the shape of the
support region near the boundary. Both of these procedures raise some issues of
interpretation that often are overlooked. We derive estimators that account for
edge effects under several support strategies and identify some interpretation
issues, using examples from forestry and limnology.
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