Sinkhorn Distributionally Robust Conditional Quantile Prediction with Fixed Design

This paper proposes a novel data-driven distributionally robust framework for conditional quantile prediction under the fixed design setting of the covariates, which we refer to as Sinkhorn distributionally robust conditional quantile prediction. We derive a convex programming dual reformulation of the proposed problem and further develop a conic optimization reformulation for the case with finite support. Our method's superior performance is demonstrated through several numerical experiments, highlighting its effectiveness in practical applications.