A0682
Title: Limit theorems for semidiscrete optimal transport maps
Authors: Kengo Kato - Cornell University (United States) [presenting]
Ziv Goldfeld - Cornell University (United States)
Ritwik Sadhu - Cornell University (United States)
Abstract: Statistical inference is studied for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. Limit distributions are derived for the $L^p$-estimation error with arbitrary $p \in [1,\infty)$ and for linear functionals of the empirical OT map. The former has a non-Gaussian limit, while the latter attains asymptotic normality. For both cases, consistency of the nonparametric bootstrap is also established. The derivation of the limit theorems relies on new stability estimates of functionals of the OT map with respect to the dual potential vector, which could be of independent interest.
