Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning
This work addresses bias issues in distributionally robust estimators for statistical learning, which is incremental as it builds on existing methods to improve accuracy.
The authors tackled the asymptotic bias of the classic Wasserstein distributionally robust estimator in statistical learning by proposing an adjusted version that is asymptotically unbiased, leading to a smaller asymptotic mean squared error, with numerical experiments showing favorable practical performance.
We propose an adjusted Wasserstein distributionally robust estimator -- based on a nonlinear transformation of the Wasserstein distributionally robust (WDRO) estimator in statistical learning. The classic WDRO estimator is asymptotically biased, while our adjusted WDRO estimator is asymptotically unbiased, resulting in a smaller asymptotic mean squared error. Further, under certain conditions, our proposed adjustment technique provides a general principle to de-bias asymptotically biased estimators. Specifically, we will investigate how the adjusted WDRO estimator is developed in the generalized linear model, including logistic regression, linear regression, and Poisson regression. Numerical experiments demonstrate the favorable practical performance of the adjusted estimator over the classic one.