Approximations to Permutation Tests of Independence Between Random Vectors

• Activity Number: 679
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Royal Statistical Society
• Author(s): Martin Bilodeau and Aurelien Guetsop*
• Companies: and Université de Montréal
• Keywords: Characteristic function ; distance covariance ; Hilbert-Schmidt independence criterion ; independence ; permutation test

Abstract

The main result establishes the equivalence in terms of power between the alpha-distance covariance test and the Hilbert-Schmidt independence criterion (HSIC) test with the characteristic kernel of a stable probability distribution of index alpha with a sufficiently small bandwidth. Large-scale simulations reveal the superiority of these two tests over other tests based on the empirical independence copula process. They also establish the usefulness of the lesser known Pearson type III approximation to the exact permutation distribution. This approximation yields tests with more accurate type I error rates than the gamma approximation usually used for HSIC, especially when dimensions of the two vectors are large. A new method for bandwidth selection in HSIC tests is proposed which improves power performance in three simulations, two of which are from machine learning. Tests of mutual independence between more than two vectors will also be discussed.