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Bayesian estimation in a multidimensional diffusion model with high frequency data

Hoffmann, Marc; Ray, Kolyan (2022), Bayesian estimation in a multidimensional diffusion model with high frequency data. https://basepub.dauphine.psl.eu/handle/123456789/24080

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
56
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Author(s)
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ray, Kolyan
Abstract (EN)
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.
Subjects / Keywords
multidimensional diffusions; high-frequency data; Gaussian processes; penalized least squares estimator