Maximum likelihood estimation and prediction error for a Matérn model on the circle

Estimation par maximum de vraisemblance et erreur de prédiction pour 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 Gaussian process interpolation with a periodized version of the Matérn covariance function (Stein, 1999, Section 6.7) with Fourier coefficients φ(α^2 + j^2)^(−ν−1/2). Convergence rates are studied for the joint maximum likelihood estimation of ν and φ when the data is 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 "deterministic" element of a continuous Sobolev space is also considered, suggesting that bounding assumptions on some parameters can lead to different estimates.

Domains: Statistics [math.ST]

Sébastien Petit. Maximum likelihood estimation and prediction error for a Matérn model on the circle. 2022. ⟨hal-03778527v3⟩