Efficiently estimating some common geostatistical models from «image-type, possibly incomplete» datasets: the R-package CGEMEV and its extension to unknown nugget-effect
Résumé
TWe consider the problem of fitting an isotropic zero-mean stationary Gaussian field model to observations on a 2-dimensional grid, possibly incomplete, when the model belongs to the Matérn family with known regularity index. The common 3 parameters of such a model are then: the inverse-range parameter theta, the variance of the signal and the signal-to-noise ratio («noise» means here « i.i.d. errors present in the observations» and thus covers the well-known nugget-effect). Assuming that the variance of the noise is known, CGEM-EV (acronym for "Conditional Gibbs-Energy Mean and Empirical Variance ») is an estimating equation in theta where the occurence of the last 2 parameters are replaced by (very quick) estimates which are functions of the noise-variance. CGEMEV has proved to be nearly as efficient as maximum likelihood (ML) in many settings ([1-2]). We propose to extend CGEMEV to the case of unknown noise-variance by adding a second equation which is the ML equation for the noise-variance if both the range parameter and the signal-to-noise ratio were known. This extension, that we call CGEMEV-EL3, has already proved to be quite useful in a very simple 1D setting: see [3]. An experimental assessment of CGEMEV-EL3 in the 2D settings of the CGEMEV package will be presented.
[1] Didier A. Girard (2017), "Efficiently Estimating Some Common Geostatistical Models by ‘Energy–Variance Matching’ or Its Randomized ‘Conditional–Mean’ Versions," Spatial Statistics, 21 pp. 1–26. doi:10.1016/j.spasta.2017.01.001.
[2] Rémy Drouilhet, Didier. A. Girard. "Estimating a Centered Isotropic Matérn Field from a (Possibly Incomplete and Noisy) Lattice Observation." github.com/didiergirard/CGEMEV.
[3] Didier A. Girard (2018). "Estimators of a Noisy Centered Ornstein-Uhlenbeck Process and Its Noise Variance" http://demonstrations.wolfram.com/
[1] Didier A. Girard (2017), "Efficiently Estimating Some Common Geostatistical Models by ‘Energy–Variance Matching’ or Its Randomized ‘Conditional–Mean’ Versions," Spatial Statistics, 21 pp. 1–26. doi:10.1016/j.spasta.2017.01.001.
[2] Rémy Drouilhet, Didier. A. Girard. "Estimating a Centered Isotropic Matérn Field from a (Possibly Incomplete and Noisy) Lattice Observation." github.com/didiergirard/CGEMEV.
[3] Didier A. Girard (2018). "Estimators of a Noisy Centered Ornstein-Uhlenbeck Process and Its Noise Variance" http://demonstrations.wolfram.com/
Origine | Fichiers produits par l'(les) auteur(s) |
---|