Preprint #98-2
KRIGING WITH NONPARAMETRIC VARIANCE FUNCTION ESTIMATION
by
J. D. Opsomer, Iowa State University
D. Ruppert, Cornell University
M. P. Wand, Harvard University
U. Holst, University of Lund
O. Hossjer, University of Lund
ABSTRACT
A method for fitting regression models to data that exhibit spatial correlation
and heteroskedasticity is proposed. A combination of parametric and nonparametric
regression techniques is used to iteratively estimate the various components
of the model. The approach is demonstrated on a large dataset of predicted
nitrogen runoff from agricultural lands in the Midwest and Northern Plains
regions of the U.S. For this dataset, the model is comprised of three main
components: (1) the mean function which includes farming practice variables,
local soil and climate characteristics and the nitrogen application treatment,
is assumed linear in the parameters and fitted generalized least squares,
(2) the variance function, which contains a local as well as a spatial
component whose shapes are left unspecified, is estimated by local linear
regression, and (3) the spatial correlation function is estimated by fitting
a parametric variogram model to the standardized residuals and after adjusting
the variogram for the presence of heteroskedasticity. The fitting
of these three components is iterated until convergence. The model provides
an improved fit to the data compared to a previous model that ignored the
heteroskedasticity and the spatial correlation.
Copies of preprints are available from the author upon request.
Use the preprint number (top right hand corner of the
abstract) and make the request directly to the author, Iowa State University,
Department of Statistics, Snedecor Hall,
Ames, IA 50011-1210.