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Kriging with Nonparametric Variance Function Estimation

Opsomer, Jean; Ruppert, David; Wand, Matt; Holst, Ulla LU and Hössjer, Ola LU (1999) In Biometrics 55(3). p.704-710
Abstract
A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity 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 heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously 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... (More)
A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity 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 heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
metamodel, Heteroscedasticity, local linear estimation, runoff modeling, spatial correlation
in
Biometrics
volume
55
issue
3
pages
704 - 710
publisher
INTERNATIONAL BIOMETRIC SOC,
external identifiers
  • scopus:0032887753
ISSN
0006-341X
DOI
10.1111/j.0006-341X.1999.00704.x
language
English
LU publication?
yes
id
da318ca0-63a8-4f4b-9dd8-55031787ff92 (old id 1244972)
alternative location
http://www3.interscience.wiley.com/cgi-bin/fulltext/119062003/PDFSTART
date added to LUP
2008-10-13 10:49:27
date last changed
2017-05-14 04:08:18
@article{da318ca0-63a8-4f4b-9dd8-55031787ff92,
  abstract     = {A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity 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 heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously 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.},
  author       = {Opsomer, Jean and Ruppert, David and Wand, Matt and Holst, Ulla and Hössjer, Ola},
  issn         = {0006-341X},
  keyword      = {metamodel,Heteroscedasticity,local linear estimation,runoff modeling,spatial correlation},
  language     = {eng},
  number       = {3},
  pages        = {704--710},
  publisher    = {INTERNATIONAL BIOMETRIC SOC,},
  series       = {Biometrics},
  title        = {Kriging with Nonparametric Variance Function Estimation},
  url          = {http://dx.doi.org/10.1111/j.0006-341X.1999.00704.x},
  volume       = {55},
  year         = {1999},
}