A nonparametric covariance estimator for spatial models
Torgny Lindström
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003
ISSN 14039338

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.



Key words:

Bivariate local polynomial regression, heteroscedastic data, local bandwidths,
nonstationary model, smoother matrix
