Permutation testing: Non-uniform sampling and minimax optimality

Speaker's Name: Tom Berrett
Speaker's Affiliation: University of Warwick
Speaker's Research Theme(s): Statistics and Probability,
Abstract:
Permutation tests have been studied since the birth of modern statistics, and are currently widely used for problems such as two-sample and independence testing. Not requiring knowledge of asymptotic distributions or strong unverifiable modelling assumptions, their appeal lies in their conceptual simplicity and strong validity guarantees. However, while Type I error control is typically easy to establish, power guarantees are usually much harder to prove. Moreover, traditional permutation tests can only be applied in problems where the null hypothesis implies a suitable notion of exchangeability. In this talk I will talk about recent work in this area establishing finite-sample power guarantees for independence testing, extending permutation methods to conditional independence problems via the use of non-uniform permutation distributions and recent results providing a new understanding of the power properties of non-uniform permutation tests.

Venue: MATHS A17