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Kriging with Nonparametric Variance Function Estimation
Author(s) -
Opsomer J. D.,
Ruppert D.,
Wand M. P.,
Holst U.,
Hössjer O.
Publication year - 1999
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.1999.00704.x
Subject(s) - heteroscedasticity , statistics , mathematics , variance function , econometrics , parametric statistics , variogram , nonparametric regression , kriging , nonparametric statistics , data set , regression analysis
Summary. A method for fitting regression models to data that exhibit spatial correlation and heteroskedas‐ticity is proposed. It is well known that ignoring a nonconstant variance does not bias least‐squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedas‐ticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms canseriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. 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 data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and 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, with the standardization 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 with a previous model that ignored the heteroskedasticity and the spatial correlation.