A test for independence of two multivariate samples

The paper presents a new nonparametric test for independence of two vectors. The idea is based on zonotope approach by G. Koshevoy, H. Oja and others, see [4, 5]. Under the independence hypothesis the test statistic converges in distribution to the supremum of a certain Gaussian field, and its asymptotic distribution is found using the theory of extrema of random Gaussian fields developed by V. Piterbarg and Yu. Tyurin, see [6, 8]. In contrast to traditional correlation coefficients the formula is not symmetric.