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Pré-Publication, Document De Travail Année : 2022

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.
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Dates et versions

hal-03913295 , version 1 (26-12-2022)

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  • HAL Id : hal-03913295 , version 1

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Marc Hoffmann, Kolyan Ray. BAYESIAN ESTIMATION IN A MULTIDIMENSIONAL DIFFUSION MODEL WITH HIGH FREQUENCY DATA. 2022. ⟨hal-03913295⟩
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