[Missing Data] Wasserstein Distributionally Robust Linear Quantile Regression on Missing Data (with Yanqin Fan and Gaoqian Xu)
in Keep calm and do research on Distributionally robust optimization, Missing data, Quantile regression Last modified at:
This paper proposes a Distributionally Robust (DR) linear quantile estimator to handle deviations from the “Missing At Random” (MAR) assumption in incomplete data. While MAR-based estimators can perform poorly when the missingness mechanism deviates from MAR, fully assumption-free approaches yield overly conservative bounds. To address this, we introduce a distributionally robust optimization framework using the Wasserstein distance to measure departures from the MAR distribution. The estimator solves a minimax optimization problem by maximizing the worst-case expected loss over a Wasserstein ball and minimizing it with respect to the parameter of interest.
