21734 articles – 15570 references  [version française]
 HAL: hal-00413693, version 2
 arXiv: 0909.1046
 Available versions: v1 (2009-09-05) v2 (2012-01-02)
 Asymptotic near-efficiency of the "Gibbs-energy and empirical-variance" estimating functions for fitting Matern models to a dense (noisy) series
 (2011-12-29)
 Let us call as ''Gaussian Gibbs energy" the quadratic form appearing 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 Matérn family with known "regularity'' index $\nu \geq 1/2$. For estimating the range and the variance of $Z$ from observations on a "dense'' regular grid, corrupted by a Gaussian white noise of known variance, 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 squared error of the resulting CGEM-EV estimate of the range-parameter to 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. This latter condition on $\nu$ has not to be imposed to obtain the convergence to 1 of the analog ratio for the microergodic-parameter. Possible extensions of this approach, which may benefit from very easy numerical implementations, 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
 Subject : Statistics/Statistics TheoryMathematics/StatisticsStatistics/Methodology
 Keyword(s): ARMA – Gaussian process – Maximum likelihood – Estimating functions – Matern autocorrelation
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 hal-00413693, version 2 http://hal.archives-ouvertes.fr/hal-00413693 oai:hal.archives-ouvertes.fr:hal-00413693 From: Didier A. Girard <> Submitted on: Saturday, 31 December 2011 18:08:00 Updated on: Monday, 2 January 2012 17:48:32