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-$\kappa$ 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.
- Award ID(s):
- 1915967
- PAR ID:
- 10285212
- Date Published:
- Journal Name:
- Quantifying the Empirical Wasserstein Distance to a Set of Measures: Beating the Curse of Dimensionality
- Volume:
- 33
- Issue:
- 2020
- Page Range / eLocation ID:
- 21260--21270
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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