Multivariate tests of associations based on univariate tests

03/08/2016 - 15:30
03/08/2016 - 16:30
Ruth Heller, Tel-Aviv University
Room 1205, Burnside Hall, 805 Sherbrooke West

 For testing two random vectors for independence, we consider testing whether the distance of one vector from an arbitrary center point is independent from the distance of the other vector from an arbitrary center point by a univariate test. We provide conditions under which it is enough to have a consistent univariate test of independence on the distances to guarantee that the power to detect dependence between the random vectors increases to one, as the sample size increases. These conditions turn out to be minimal. If the univariate test is distribution-free, the multivariate test will also be distribution-free. If we consider multiple center points and aggregate the center-specific univariate tests, the power may be further improved. We suggest a specific aggregation method for which the resulting multivariate test will be distribution-free if the univariate test is distribution-free. We show that several multivariate tests recently proposed in the literature can be viewed as instances of this general approach.

Last edited by on Thu, 03/31/2016 - 15:40