  Robust estimation is an important problem in statistics which aims at
providing a reasonable estimator when the data-generating distribution lies
within an appropriately defined ball around an uncontaminated distribution.
Although minimax rates of estimation have been established in recent years,
many existing robust estimators with provably optimal convergence rates are
also computationally intractable. In this paper, we study several estimation
problems under a Wasserstein contamination model and present computationally
tractable estimators motivated by generative adversarial networks (GANs).
Specifically, we analyze properties of Wasserstein GAN-based estimators for
location estimation, covariance matrix estimation, and linear regression and
show that our proposed estimators are minimax optimal in many scenarios.
Finally, we present numerical results which demonstrate the effectiveness of
our estimators.
