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Distribution-Free Nonparametric Inference Based on Optimal Transport and Kernel Methods
The Wilcoxon rank-sum (or Mann–Whitney) test is one of the most widely used tools for comparing two groups without making assumptions about the underlying data distribution. One of the reasons for its enduring popularity is a remarkable result of Hodges and Lehmann (1956), which shows that the asymptotic relative efficiency of Wilcoxon’s test with respect to Student’s t-test, under location alternatives, never falls below 0.864, despite the former being 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 other words, the Gaussian score transformed Wilcoxon test uniformly dominates the t-test in terms of efficiency, while also remaining distribution-free.
In this talk we will discuss multivariate versions of these celebrated results, by considering distribution-free analogues of the Hotelling T²-test based on optimal transport. The proposed tests are consistent against a general class of alternatives and satisfy Hodges-Lehmann and Chernoff-Savage-type efficiency lower bounds over various natural families of multivariate distributions, despite being entirely agnostic to the underlying data generating mechanism. We will also discuss how optimal-transport-based multivariate ranks can be used to construct distribution-free analogues of the celebrated kernel two-sample test that enjoy a trifecta of desirable properties: universal consistency, efficient computation, and nontrivial asymptotic efficiency.
Date:
5 March 2026, 15:30
Venue:
24-29 St Giles', 24-29 St Giles' OX1 3LB
Venue Details:
Large Lecture Theatre, Department of Statistics
Speaker:
Professor Bhaswar B. Bhattacharya (The Wharton School, University of Pennsylvania)
Organising department:
Department of Statistics
Organisers:
Beverley Lane (Department of Statistics, University of Oxford),
Professor Simon Myers (University of Oxford)
Organiser contact email address:
events@stats.ox.ac.uk
Hosts:
Professor Frank Windmeijer (University of Oxford),
Professor Simon Myers (University of Oxford)
Booking required?:
Required
Booking url:
https://www.stats.ox.ac.uk/events/distinguished-speaker-seminar
Booking email:
events@stats.ox.ac.uk
Cost:
No charge
Audience:
Members of the University only
Editor:
Beverley Lane
