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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
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Official URL: https://doi.org/10.1093/imaiai/iaz003
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics Faculty of Science > Statistics |
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| 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 | ||||||||
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| Volume: | 8 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 657-676 | ||||||||
| DOI: | 10.1093/imaiai/iaz003 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Publisher Statement: | 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 | ||||||||
| RIOXX Funder/Project Grant: |
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