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CATEGORIES:Statistics
SUMMARY:Distribution-Free Nonparametric Inference Based on
Optimal Transport: Efficiency Lower Bounds and Ra
nk-Kernel Tests - Bhaswar Bhattacharya\, Universit
y of Pennsylvania
DTSTART;TZID=Europe/London:20210521T160000
DTEND;TZID=Europe/London:20210521T170000
UID:TALK159745AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/159745
DESCRIPTION:The Wilcoxon rank-sum/Mann-Whitney test is one of
the most popular distribution-free procedures for
testing the equality of two univariate probability
distributions. One of the main reasons for its po
pularity can be attributed to the remarkable resul
t of Hodges and Lehmann (1956)\, which shows that
the asymptotic relative efficiency of Wilcoxon's t
est with respect to Student's t-test\, under locat
ion alternatives\, never falls below 0.864\, despi
te the former being exactly distribution-free in f
inite samples. Even more striking is the result of
Chernoff and Savage (1958)\, which shows that the
efficiency of a Gaussian score transformed Wilcox
on's test\, against the t-test\, is lower bounded
by 1. In this talk we will discuss multivariate ve
rsions of these celebrated results\, by considerin
g distribution-free analogues of the Hotelling T^2
-test based on optimal transport. The proposed tes
ts are consistent against a general class of alter
natives and satisfy Hodges-Lehmann and Chernoff-Sa
vage-type efficiency lower bounds over various nat
ural families of multivariate distributions\, desp
ite being entirely agnostic to the underlying data
generating mechanism. Analogous results for indep
endence testing will also be presented. Finally\,
we will discuss how optimal transport based multiv
ariate ranks can be used to obtain distribution-fr
ee kernel two-sample tests\, which are universally
consistent\, computationally efficient\, and have
non-trivial asymptotic efficiency.\n\n(Based on j
oint work with Nabarun Deb and Bodhisattva Sen.)
LOCATION: https://maths-cam-ac-uk.zoom.us/j/95871364531?pwd
=aFZaV0loSWt6QmRDbm5ONWNjTTBjZz09
CONTACT:Dr Sergio Bacallado
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