On parameter estimation with the Wasserstein distance
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 approximation of these estimators and illustrate their behavior in several numerical experiments. Two of our examples are taken from the literature on approximate Bayesian computation and have likelihood functions that are not analytically tractable. Two other examples involve misspecified models.
Cite
@article{arxiv.1701.05146,
title = {On parameter estimation with the Wasserstein distance},
author = {Espen Bernton and Pierre E. Jacob and Mathieu Gerber and Christian P. Robert},
journal= {arXiv preprint arXiv:1701.05146},
year = {2019}
}
Comments
29 pages (+18 pages of appendices), 6 figures. To appear in Information and Inference: A Journal of the IMA. A previous version of this paper contained work on approximate Bayesian computation with the Wasserstein distance, which can now be found at arxiv:1905.03747