BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Distribution-Free Nonparametric Inference Based on Optimal Transpo
 rt: Efficiency Lower Bounds and Rank-Kernel Tests - Bhaswar Bhattacharya\,
  University of Pennsylvania
DTSTART:20210521T150000Z
DTEND:20210521T160000Z
UID:TALK159745@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:The Wilcoxon rank-sum/Mann-Whitney test is one of the most pop
 ular distribution-free procedures for testing the equality of two univaria
 te probability distributions. One of the main reasons for its popularity c
 an be attributed to the remarkable result of Hodges and Lehmann (1956)\, w
 hich shows that the asymptotic relative efficiency of Wilcoxon's test with
  respect to Student's t-test\, under location alternatives\, never falls b
 elow 0.864\, despite the former being exactly distribution-free in finite 
 samples. Even more striking is the result of Chernoff and Savage (1958)\, 
 which shows that the efficiency of a Gaussian score transformed Wilcoxon's
  test\, against the t-test\, is lower bounded by 1. In this talk we will d
 iscuss multivariate versions of these celebrated results\, by considering 
 distribution-free analogues of the Hotelling T^2-test based on optimal tra
 nsport. The proposed tests are consistent against a general class of alter
 natives and satisfy Hodges-Lehmann and Chernoff-Savage-type efficiency low
 er bounds over various natural families of multivariate distributions\, de
 spite being entirely agnostic to the underlying data generating mechanism.
  Analogous results for independence testing will also be presented. Finall
 y\, we will discuss how optimal transport based multivariate ranks can be 
 used to obtain distribution-free kernel two-sample tests\, which are unive
 rsally consistent\, computationally efficient\, and have non-trivial asymp
 totic efficiency.\n\n(Based on joint work with Nabarun Deb and Bodhisattva
  Sen.)
LOCATION: https://maths-cam-ac-uk.zoom.us/j/95871364531?pwd=aFZaV0loSWt6Qm
 RDbm5ONWNjTTBjZz09
END:VEVENT
END:VCALENDAR