# Minimum Wasserstein distance estimator under covariate shift: closed-form, super-efficiency and irregularity

arXiv: https://arxiv.org/abs/2601.07282 · HTML: https://mlsanity.com/paper/2601.07282/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 61 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [OpenML-Python: an extensible Python API for OpenML](https://mlsanity.com/paper/1911.02490/) (2019)
- [Robust Importance Weighting for Covariate Shift](https://mlsanity.com/paper/1910.06324/) (2019)
- [Augmented Transfer Regression Learning with Semi-non-parametric Nuisance Models](https://mlsanity.com/paper/2010.02521/) (2020)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [Double-Weighting for Covariate Shift Adaptation](https://mlsanity.com/paper/2305.08637/) (2023)
- [Transfer Learning with General Estimating Equations](https://mlsanity.com/paper/2410.04398/) (2024)
- [Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation](https://mlsanity.com/paper/2310.16638/) (2023)
- [Nearest Neighbor Sampling for Covariate Shift Adaptation](https://mlsanity.com/paper/2312.09969/) (2023)
- [Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data](https://mlsanity.com/paper/2107.07371/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)

## Abstract (arXiv)

Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We propose a minimum Wasserstein distance estimation framework for inference under covariate shift that avoids explicit modeling of outcome regressions or importance weights. The resulting W-estimator admits a closed-form expression and is numerically equivalent to the classical 1-nearest neighbor estimator, yielding a new optimal transport interpretation of nearest neighbor methods. We establish root-n asymptotic normality and show that the estimator is not asymptotically linear, leading to super-efficiency relative to the semiparametric efficient estimator under covariate shift in certain regimes, and uniformly in missing data problems. Numerical simulations, along with an analysis of a rainfall dataset, underscore the exceptional performance of our W-estimator.