HAL : hal-00413693, version 1

arXiv : 0909.1046

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Asymptotic near-efficiency of a "Gibbs-energy" estimating function approach for fitting Matern covariance models to a dense (noisy) series

Didier A. Girard 1

(04/09/2009)

Let us call “Gibbs energy” the quadratic form occurring in the maximum likelihood (ML) criterion when fitting a zero-mean multidimensional Gaussian distribution to one realization. We consider a continuous-time Gaussian process Z which belongs to the Matern family with known regularity index $\nu$ ≥ 1/2. For estimating the range and the variance of Z from noisy observations on a dense regular grid, we propose two simple estimating functions based on the conditional Gibbs energy mean (CGEM) and the empirical variance (EV). We show that the ratio of the large sample mean square error of the CGEM-EV estimate of the range-parameter over the one of its ML estimate, and the analog ratio for the variance-parameter, both converge (when the grid-step tends to 0) toward a constant, only function of $\nu$, surprisingly close to 1 provided $\nu$ is not too large. Extensions of this approach, which may enjoy a very easy numerical implementation, are briefly discussed.

1 :	Laboratoire Jean Kuntzmann (LJK)
	CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

Domaine

:

Statistiques/Théorie Mathématiques/Statistiques Statistiques/Méthodologie

Mots Clés : ARMA – Gaussian process – Maximum likelihood – Estimating functions – Matern autocorrelation

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Contributeur : Didier A. Girard <>

Soumis le : Samedi 5 Septembre 2009, 19:39:01

Dernière modification le : Samedi 5 Septembre 2009, 20:40:37