%0 Journal Article
%A Pelletier, B.
%A Dutilleul, P.
%A Larocque, G.
%A Fyles, J.W.
%T Fitting the linear model of coregionalization by generalized least squares
%B Mathematical Geology
%D 2004
%V 36
%P 323-344
%N 3
%Z cited By 29; doi=(10.1023/B:MATG.0000028440.29965.2d)
%X In geostatistical studies, the fitting of the linear model of coregionalization
(LMC) to direct and cross experimental semivariograms is usually
performed with a weighted least-squares (WLS) procedure based on
the number of pairs of observations at each lag. So far, no study
has investigated the efficiency of other least-squares procedures,
such as ordinary least squares (OLS), generalized least squares (GLS),
and WLS with other weighing functions, in the context of the LMC.
In this article, we compare the statistical properties of the sill
estimators obtained with eight least-squares procedures for fitting
the LMC: OLS, four WLS, and three GLS. The WLS procedures are based
on approximations of the variance of semivariogram estimates at each
distance lag. The GLS procedures use a variance-covariance matrix
of semivariogram estimates that is (i) estimated using the fourth-order
moments with sill estimates (GLS 1), (ii) calculated using the fourth-order
moments with the theoretical sills (GLS 2), and (iii) based on an
approximation using the correlation between semivariogram estimates
in the case of spatial independence of the observations (GLS 3).
The current algorithm for fitting the LMC by WLS while ensuring the
positive semidefiniteness of sill matrix estimates is modified to
include any least-squares procedure. A Monte Carlo study is performed
for 16 scenarios corresponding to different combinations of the number
of variables, number of spatial structures, values of ranges, and
scale dependence of the correlations among variables. Simulation
results show that the mean square error is accounted for mostly by
the variance of the sill estimators instead of their squared bias.
Overall, the estimated GLS 1 and theoretical GLS 2 are the most efficient,
followed by the WLS procedure that is based on the number of pairs
of observations and the average distance at each lag. On that basis,
GLS 1 can be recommended for future studies using the LMC. © 2004
International Association for Mathematical Geology.
Scopus
%( 08828121
%K geostatistics; least squares method; mathematical analysis
%U http://www.scopus.com/inward/record.url?eid=2-s2.0-3042803149&partnerID=40&md5=9a69c7c0cb328c2a9bc30d37a88d3a15
%F PelletierDutilleulLarocqueEtAl2004
%3 BibTeX type = ARTICLE