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Automatic variogram modeling by iterative least squares. Univariate and multivariate cases.

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Didier Renard

Résumé

In this paper, we propose a new methodology to automatically find a model that fits on an experimental variogram. Starting with a linear com- bination of some basic authorized structures (e.g spherical, exponential,...), a numerical algorithm is used to compute the parameters which minimize a distance between the model and the experimental variogram. The initial values are automatically chosen and the algorithm is iterative. After this first step, parameters with a negligible influence are discarded from the model and the more parsimonious model is estimated by using the numerical algorithm again. This process is iterated until no more parameter can be discarded. A procedure based on a profiled cost function is also developped in order to use the numerical algorithm for multivariate data sets (possibly with a lot of variables) modeled in the scope of a linear model of coregionalization. The efficiency of the method is illustrated on several examples (including variogram maps) and on a multivariate case study.
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Dates et versions

hal-00707887 , version 1 (13-06-2012)
hal-00707887 , version 2 (25-09-2012)

Identifiants

  • HAL Id : hal-00707887 , version 2

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Nicolas Desassis, Didier Renard. Automatic variogram modeling by iterative least squares. Univariate and multivariate cases.. 2012. ⟨hal-00707887v2⟩
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