Prediction of Spatial Cumulative Distribution Functions Using Subsampling

The 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 article we develop a spatial subsampling method for predicting an SCDF based on observations made on a hexagonal grid, similar to...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1999-03, Vol.94 (445), p.86-97
Main Authors: Lahiri, Soumendra N., Kaiser, Mark S., Cressie, Noel, Hsu, Nan-Jung
Format: Article
Language:English
Subjects:
Cumulative distribution functions
Ecoregions
Empirical research
Environmental monitoring
Environmental protection
Estimators
Forest ecology
Increasing domain asymptotics
Infill asymptotics
Integers
Leaves
Maine
Population estimates
Sampling
Simultaneous prediction intervals
Spatial distribution
Spatial subsampling
Theory and Methods
Time series
Trees
U.S.A
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Summary:The 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 article 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 quite 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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1999.10473821