A Remark on the Use of a Weight Matrix in the Linear Model of Coregionalization |
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Authors: | Samuel D Oman Bella Vakulenko-Lagun |
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Institution: | (1) Department of Natural Resource Sciences, McGill University, Macdonald Campus, Ste-Anne-de-Bellevue, QC, H9X 3V9, Canada;(2) Department of Plant Science, McGill University, Macdonald Campus, Ste-Anne-de-Bellevue, QC, H9X 3V9, Canada |
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Abstract: | The linear model of coregionalization (LMC) is generally fit to multivariate geostatistical data by minimizing a least-squares
criterion. It is commonly believed that weighting the criterion by inverse variances will reduce the influence of those variables
with large variance. We point out that this need not be so, and that in some cases the weights will have no effect whatsoever
on the estimated sill matrices. When there is an effect, it is due not to a reduction of these variables’ influence, but rather
due to a lack of invariance of the minimization problem; moreover, sometimes the influence may actually increase. The correct
way to reduce influence is to fit the LMC after standardizing the variables to have unit variance. |
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