Asymptotic analysis for covariance parameter estimation of Gaussian processes with functional inputs
Résumé
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend these theoretical guarantees to encompass scenarios accounting for approximation errors in the inputs, which allows robustness of practical implementations relying on conventional sampling methods or projections onto a functional basis. Loosely speaking, both consistency and normality hold when the approximation error becomes negligible, a condition that is often achieved as the number of samples or basis functions becomes large. These later asymptotic properties are illustrated through analytical examples, including one that covers the case of non-randomly perturbed grids, as well as several numerical illustrations.
Mots clés
parametric statistics
increasing-domain asymptotics
functional data
Gaussian processes
maximum likelihood estimator
asymptotic consistency
asymptotic normality
parametric statistics increasing-domain asymptotics functional data Gaussian processes maximum likelihood estimator asymptotic consistency asymptotic normality. Mathematics Subject Classification (2020): 60G15 62F12 62R10
parametric statistics
asymptotic normality. Mathematics Subject Classification (2020): 60G15
62F12
62R10
parametric statistics
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)