Preprint #96-4
Prediction of Spatial Cumulative Distribution Functions
Using Subsampling
by
S.N. Lahiri, M.S. Kaiser, N. Cressie and N.-J. Hsu
Abstract
A Spatial Cumulative Distribution Function (SCDF) is a random function
that provides a statistical summary of a random field over a spatial domain
of interest. In this paper we develop a spatial subsampling method for
predicting an SCDF based on observations made on a hexagonal grid, similar
to the one used in the Environmental Monitoring and Assessment Program
of the U.S. Environmental Protection Agency. We show that, under fairly
general conditions, the proposed subsampling method provides accurate
data-based approximations to the sampling distributions of various
functionals of the SCDF predictor. In particular, it produces estimators
of different population characteristics, such as the quantiles and weighted
mean integrated squared errors of the empirical predictor. As an
illustration, we apply the subsampling method to construct large sample
prediction bands for the SCDF of an ecological index for foliage
condition of Red Maple trees in the state of Maine, USA.
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University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.