The classical LePage and 5 variants of it are performed, as proposed by Hussain and Tsagris (2025).
The test is performed for each pair of columns of the x and y matrices, between the i-th column of and y.
References
Hussain A. and Tsagris M. (2025). Modified Lepage-type test statistics for the weak null hypothesis.
https://arxiv.org/pdf/2509.19126