Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning

We propose an adjusted Wasserstein distributionally robust estimator -- based on a nonlinear transformation of the Wasserstein distributionally robust (WDRO) estimator in statistical learning. This transformation will improve the statistical performance of WDRO because the adjusted WDRO estimator is asymptotically unbiased and has an asymptotically smaller mean squared error. The adjusted WDRO will not mitigate the out-of-sample performance guarantee of WDRO. Sufficient conditions for the existence of the adjusted WDRO estimator are presented, and the procedure for the computation of the adjusted WDRO estimator is given. Specifically, we will show how the adjusted WDRO estimator is developed in the generalized linear model. Numerical experiments demonstrate the favorable practical performance of the adjusted estimator over the classic one.