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.


Copies of preprints are available from the author upon request. Use the preprint number (located at the top of the page) and make the request directly to the author, Iowa State University, Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.