Nonparametric Bayesian estimation in a multidimensional diffusion model with high frequency data
Author(s)
Hoffmann, Marc
Ray, Kolyan
Type
Journal Article
Abstract
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a gen eral posterior contraction rate theorem in L2-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 Holder 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.
posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over Holder 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.
Date Issued
2025-02-01
Date Acceptance
2024-09-03
Citation
Probability Theory and Related Fields, 2025, 191, pp.103-180
ISSN
0178-8051
Publisher
Springer
Start Page
103
End Page
180
Journal / Book Title
Probability Theory and Related Fields
Volume
191
Copyright Statement
© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s00440-024-01317-w
Subjects
Bayesian nonparametrics
Multidimensional diffusions
High-frequency data
Gaussian processes
Penalized least squares estimator Mathematics Subject Classification 62G20
62F15
60J60
Publication Status
Published
Date Publish Online
2024-10-07