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Communication Dans Un Congrès Année : 2015

An experimental assessment of the "Gibbs-Energy and Empirical-Variance" estimating equations (via Kalman smoothing) for Matérn processes

Didier A. Girard

Résumé

The problem of estimating (from n noisy observations of a single realization, at known sites) the parameters of a centered stationary Gaussian process whose autocorrelation function belongs to the Matérn class appears in many contexts (e.g. [1, 2, 3]). The recently proposed CGEM-EV method [4] only requires the computation of several conditional means, at the observation sites, corresponding to candidate values for the Matérn parameters. In dimension 1 and when the “Matérn differentiability” parameter is fixed to k + 1/2 with k integer (an often-used value is k = 0 or k = 1, see e.g. [3], [1], [6], [7], [8]), each of these conditional means reduces to a Kalman smoothing. An R implementation of CGEM-EV for this context is presented : it is built on the R-package dlm [5]. It proves to be quite fast, even for high-frequency sampling (e.g. n = 8196), and an empirical comparison with the classical maximum likelihood estimator confirms the near- efficiency results of [4].
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hal-01229334 , version 1 (19-12-2018)

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  • HAL Id : hal-01229334 , version 1

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Didier A. Girard. An experimental assessment of the "Gibbs-Energy and Empirical-Variance" estimating equations (via Kalman smoothing) for Matérn processes. Quatrièmes rencontres R (4th R meeting ), Jun 2015, Grenoble, France. ⟨hal-01229334⟩
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