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A nonparametric covariance estimator for spatial models

Lindström, Torgny LU (2003) In Preprint without journal information
Abstract
The covariances in spatial models are estimated by linear smoothing of products of residuals. In the model no parametric assumptions are made about the mean function or the spatial dependence. Both are assumed to be smooth. Smoothing is based on local polynomials, though any linear smoother is possible to use. Expressions for the mean and the covariance of this estimator are developed and a version that corrects for bias is proposed. Note that the covariance estimates generated by this method are not guaranteed to be positive definite, though proper covariance function estimates can be generated by known methods. The advantage with the covariance estimation described here is that the procedure might allow for testing of stationarity prior... (More)
The covariances in spatial models are estimated by linear smoothing of products of residuals. In the model no parametric assumptions are made about the mean function or the spatial dependence. Both are assumed to be smooth. Smoothing is based on local polynomials, though any linear smoother is possible to use. Expressions for the mean and the covariance of this estimator are developed and a version that corrects for bias is proposed. Note that the covariance estimates generated by this method are not guaranteed to be positive definite, though proper covariance function estimates can be generated by known methods. The advantage with the covariance estimation described here is that the procedure might allow for testing of stationarity prior to the fitting of a stationary covariance function. Simulation studies are performed to observe the estimator both for a stationary and isotropic, and a heteroscedastic model. We show good agreement between numerical and theoretical results and also numerically explore the bias introduced by the different smoothers used in the estimation procedure. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
in
Preprint without journal information
issue
2003:2
publisher
Manne Siegbahn Institute
ISSN
0348-7911
language
English
LU publication?
yes
id
ee3a0065-60f2-4455-a962-8322c679bbc7 (old id 834484)
date added to LUP
2008-01-10 14:55:25
date last changed
2016-04-16 07:03:51
@misc{ee3a0065-60f2-4455-a962-8322c679bbc7,
  abstract     = {The covariances in spatial models are estimated by linear smoothing of products of residuals. In the model no parametric assumptions are made about the mean function or the spatial dependence. Both are assumed to be smooth. Smoothing is based on local polynomials, though any linear smoother is possible to use. Expressions for the mean and the covariance of this estimator are developed and a version that corrects for bias is proposed. Note that the covariance estimates generated by this method are not guaranteed to be positive definite, though proper covariance function estimates can be generated by known methods. The advantage with the covariance estimation described here is that the procedure might allow for testing of stationarity prior to the fitting of a stationary covariance function. Simulation studies are performed to observe the estimator both for a stationary and isotropic, and a heteroscedastic model. We show good agreement between numerical and theoretical results and also numerically explore the bias introduced by the different smoothers used in the estimation procedure.},
  author       = {Lindström, Torgny},
  issn         = {0348-7911},
  language     = {eng},
  number       = {2003:2},
  publisher    = {ARRAY(0x9b19b28)},
  series       = {Preprint without journal information},
  title        = {A nonparametric covariance estimator for spatial models},
  year         = {2003},
}