【Team】High-Dimensional Structure Theory Team
【Date】2026/September/29(Tuesday) 16:00-17:00(JST)
【Speaker】Talk by Christophe Quentin Valvason, University of Geneva
Title: Optimal Transport for Nonparametric Inference: Improving Confidence Intervals
Abstract:
Reliable statistical inference is particularly challenging in small samples, where standard
confidence procedures may exhibit substantial deviations from their nominal coverage. In this
talk, we present a novel approach to constructing nonparametric confidence intervals based on
optimal transport. The proposed method recasts confidence interval construction as an optimal
transport problem between a discrete source measure and an estimate of the sampling
distribution. We establish finite-sample bounds for the non-coverage probability, showing how
the performance of the procedure depends on the source measure through the geometry of the
associated dual potential. We further establish asymptotic validity, including consistency of the
resulting confidence intervals in the Hausdorff metric. A regularization perspective is developed
to explain how the finite support of the source measure stabilizes the interval construction. Simulation
studies illustrate the finite-sample performance of the proposed method, with coverage
probabilities generally closer to the nominal level than those of standard bootstrap procedures.
