STICERD Econometrics Seminar Series
Semidiscrete optimal transport maps: stability, limit theorems, and asymptotic efficiency
Kengo Kato (Cornell University)
Thursday 16 November 2023 14:00 - 15:30
Many of our seminars and public events this year will continue as in person or as hybrid (online and in person) events. Please check our website listings and Twitter feed @STICERD_LSE for updates.
Unless otherwise specified, in-person seminars are open to the public.
Those unable to join the seminars in-person are welcome to participate via zoom if the event is hybrid.
About this event
We study statistical inference 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. We derive limit distributions for the integral and linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. For both cases, we also establish consistency of the nonparametric bootstrap. The derivation of our limit theorems relies on new stability estimates of functionals of the OT map with respect to the dual potential vector, which may be of independent interest. We also discuss applications of our limit theorems to the construction of confidence sets for the OT map and inference for a maximum tail correlation. Finally, we discuss asymptotic efficiency of the empirical OT map in an infinite dimensional setting.
STICERD Econometrics seminars are held on Thursdays in term time at 14.00-15.30, in SAL 3.05, unless specified otherwise.
For further information please contact Sadia Ali: firstname.lastname@example.org.
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