here is a first summary of the replies I received to my first question (on the
use of resampling techniques & cross-validation techniques applied to spatial
dependent data) and that have not been sent to the list.
Thanks a lot to all who contributed.
Denis Marcotte ( Denis.Marcotte@...
"It is still an open question. Some have suggested to work with
orthogonal residuals. The problem is that the orthogonalization calls
for the covariance function which is precisely what we want to estimate with
these techniques. Journel (1994) suggested to produce conditional realizations
and then to resample from these realizations. This calls
for a knowledge of the covariance function (to use in the conditional
simulation) and of the sampling strategy used to get the original
sample that will be applied to the various realizations
(But, of course not at the same points, as these are perfectly
reproduced by the conditional simulations). Naraghi and Marcotte (1996) used
the fact that increments computed for variogram computation are rather weakly
correlated in average for small lags and when the same
data point is not used for the construction of more than one increment
for a given lag distance. They then resampled the increments within
each lag distance class. A bad idea is certainly to resample directly
the data points, as this biased strongly the covariance function toward
a pure nugget effect."
Two other references are given by Edzer Pebesma
A. Solow, bootstrapping correlated data,
Math. Geol. early eighties.
P. Kitanidis, something with `Orthogonal residuals' in the title, also
Math. Geol., year unknown.
For what concerns the use of cross-validation applied to geostatistical
data,Donald Myers writes
There have also been a couple of papers by Bruce Davis, A. Solow and
Kathryn Campbell (all in Math Geology) with warnings about the use of
The cross-validation statistics are not equally sensitive to changes in the
variogram model and or the parameters of the variogram. Some of them are
sensitive to changes in the search neighborhood. In the case of simple
kriging and cross-validation, the theoretical maximum value of the
correlation between the observed and estimated values is 1. However if
ordinary kriging is used then the theoretical maximum value is less because of
the LaGrange multiplier. Similarly if simple kriging is used the theoretical
minimum for the correlation between estimated and the
estimation error is zero, this is not true if ordinary kriging is used.
Again the LaGrange multiplier has an effect.
1992, Myers, D.E., Selection of a radial basis function for data
Advances in Computer Methods for Partial Differential Eq. VII, R.
Vichnevetsky, D. Knight and G.Richter (eds), IMACS, 553-558
1991, Myers,D.E., On Variogram Estimation. in Proceedings of the First
Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II,
American Sciences Press, 261-281
1991, Myers,D.E., Interpolation and Estimation with Spatially
Located Data, Chemometrics and Intelligent Laboratory Systems 11, 209-228
Section of Earth Sciences
Institute of Mineralogy and Petrography
University of Lausanne
Currently detached in Italy
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