Nonparametric Bayesian estimation in a multidimensional diffusion model with high frequency data
Abstract
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete highfrequency 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 Hölder 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.12267
 arXiv:
 arXiv:2211.12267
 Bibcode:
 2022arXiv221112267H
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability;
 62G20;
 62F15;
 60J60
 EPrint:
 61 pages, 1 figure, to appear in Probability Theory and Related Fields