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
TypeDocument de travail / Working paper
Series titleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / Keywordsmultidimensional diffusions; high-frequency data; Gaussian processes; penalized least squares estimator
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Hoffmann, Marc; Labadie, Mauricio; Lehalle, Charles-Albert; Pagès, Gilles; Pham, Huyên; Rosenbaum, Mathieu (2014) Article accepté pour publication ou publié