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On parameter estimation with the Wasserstein distance

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Bernton, Espen, Jacob, Pierre E., Gerber, Mathieu and Robert, Christian P. (2019) On parameter estimation with the Wasserstein distance. Information and Inference, 8 (4). pp. 657-676. doi:10.1093/imaiai/iaz003 ISSN 2049-8764.

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Official URL: https://doi.org/10.1093/imaiai/iaz003

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Abstract

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein distance estimators, complementing results derived by Bassetti, Bodini and Regazzini in 2006. In particular, our results cover the misspecified setting, in which the data-generating process is not assumed to be part of the family of distributions described by the model. Our results are motivated by recent applications of minimum Wasserstein estimators to complex generative models. We discuss some difficulties arising in the numerical approximation of these estimators. Two of our numerical examples (⁠g-and-κ and sum of log-normals) are taken from the literature on approximate Bayesian computation and have likelihood functions that are not analytically tractable. Two other examples involve misspecified models.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Estimation theory, Mathematical statistics
Journal or Publication Title: Information and Inference
Publisher: Oxford University Press
ISSN: 2049-8764
Official Date: December 2019
Dates:
DateEvent
December 2019Published
22 October 2019Available
28 January 2019Accepted
Volume: 8
Number: 4
Page Range: pp. 657-676
DOI: 10.1093/imaiai/iaz003
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This is a pre-copyedited, author-produced version of an article accepted for publication in Information and Inference following peer review. The version of record 22/10/2019 is available online at: https://doi.org/10.1093/imaiai/iaz003
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 25 March 2019
Date of first compliant Open Access: 22 October 2020
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
DMS-1712872National Science Foundationhttp://dx.doi.org/10.13039/100000001
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