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.

翻译：本文提出一种调整型Wasserstein分布鲁棒估计器——基于统计学习中Wasserstein分布鲁棒（WDRO）估计器的非线性变换。该变换将提升WDRO的统计性能，因为调整型WDRO估计量渐近无偏且具有渐近更小的均方误差。调整型WDRO不会削弱WDRO的样本外性能保证。本文给出了调整型WDRO估计量存在的充分条件，并阐述了其计算流程。具体地，我们将展示如何在广义线性模型中构建调整型WDRO估计量。数值实验表明，调整型估计器相较于经典估计器具有更优的实际性能。