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DTSTART:20241103T020000
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UID:calendar.3229.events_uoft_date.0@www.statistics.utoronto.ca
CREATED:20240610T151448Z
DESCRIPTION:\nWhen and Where: \nFriday, June 14, 2024 2:00 pm to 3:00 pm
\n 9014 \n Ontario Power Building \n 700 University Avenue, Toronto, ON
M5G 1Z5 \n\nSpeakers \nKengo Kato, Cornell University \n\nDescription: \n
We study statistical inference for the optimal transport (OT) also known a
s the Brenier map) from a known absolutely continuous reference distributi
on 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-Gaussia
n limit, whose explicit density is derived, while the latter attains asy
mptotic normality. For both cases, we also establish consistency of the n
onparametric 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 dimen
sional setting.About Kengo KatoMost recently a member of the Faculty of Ec
onomics at The University of Tokyo, Kato’s research fields are mathematic
al statistics, econometrics, and economic statistics with a focus on hig
h dimensional statistical and econometric models. He was a visiting schola
r in the Department of Economics at MIT and is the associate editor of the
Japanese Economic Review and the Journal of Statistical Planning and Infe
rence. \nMap \n700 University Avenue, Toronto, ON M5G 1Z5 \n\nCategorie
s \n Other Seminars \n\nAudiences \n FacultyGraduate Students
DTSTART;TZID=America/New_York:20240614T140000
DTEND;TZID=America/New_York:20240614T150000
LAST-MODIFIED:20240610T151559Z
LOCATION:700 University Avenue, Toronto, ON M5G 1Z5
SUMMARY:Semidiscrete Optimal Transport Maps: Stability, Limit Theorems, a
nd Asymptotic Efficiency
URL;TYPE=URI:https://www.statistics.utoronto.ca/events/semidiscrete-optimal
-transport-maps-stability-limit-theorems-and-asymptotic-efficiency
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