Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions
File(s)
Published version
Author(s)
Abdulle, Assyr
Pavliotis, Grigorios A
Zanoni, Andrea
Type
Journal Article
Abstract
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the homogenized dynamics. Our first estimator is derived from a martingale estimating function of the generator of the homogenized diffusion process. However, the unbiasedness of the estimator depends on the rate with which the observations are sampled. We therefore introduce a second estimator which relies also on filtering the data, and we prove that it is asymptotically unbiased independently of the sampling rate. A series of numerical experiments illustrate the reliability and efficiency of our different estimators.
Date Issued
2022-04-15
Date Acceptance
2022-01-20
Citation
Statistics and Computing, 2022, 32 (2), pp.1-33
ISSN
0960-3174
Publisher
Springer Science and Business Media LLC
Start Page
1
End Page
33
Journal / Book Title
Statistics and Computing
Volume
32
Issue
2
Copyright Statement
© The Author(s) 2022. Open Access 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
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://link.springer.com/article/10.1007/s11222-022-10081-7
Grant Number
EP/P031587/1
Subjects
Statistics & Probability
0104 Statistics
0802 Computation Theory and Mathematics
Publication Status
Published
Article Number
34
Date Publish Online
2022-04-11