An asymptotic study of the joint maximum likelihood estimation of the regularity and the amplitude parameters of a Matérn model on the circle

Une étude asymptotique de l'estimation par maximum de vraisemblance des paramètres de régularité et d'amplitude d'un modèle de Matérn défini sur le cercle

Sébastien Petit (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 LNE - Laboratoire National de Métrologie et d'Essais [Trappes]

This work considers parameter estimation for Gaussian process interpolation with a periodized version of the Matérn covariance function introduced by Stein. Convergence rates are studied for the joint maximum likelihood estimation of the regularity and the amplitude parameters when the data are sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a fixed deterministic element of a Sobolev space of continuous functions is also considered, suggesting that a joint estimation does not select the regularity parameter as if the amplitude were fixed.

Domaines: Statistiques [math.ST]

Sébastien Petit. An asymptotic study of the joint maximum likelihood estimation of the regularity and the amplitude parameters of a Matérn model on the circle. 2023. ⟨hal-03778527v6⟩