An asymptotic study of the joint maximum likelihood estimation of the regularity and the amplitude parameters of a periodized Matérn model
Résumé
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.
Mots clés
- Fixed-domain asymptotics
- Gaussian random field
- Matérn-type covariance function
- Regularity.
- MSC2020 subject classifications: Primary 62E20 62G20 62M30 Fixed-domain asymptotics Gaussian random field Matérn-type covariance function Regularity
- MSC2020 subject classifications: Primary 62E20
- 62G20
- 62M30 Fixed-domain asymptotics
- Regularity
Domaines
| Origine | Fichiers produits par l'(les) auteur(s) |
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