BAYESIAN ESTIMATION IN A MULTIDIMENSIONAL DIFFUSION MODEL WITH HIGH FREQUENCY DATA
Résumé
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in L 2-loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over H ölder smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)