A Wilcoxon-Mann-Whitney type test for infinite dimensional data

The Wilcoxon-Mann-Whitney test is a robust competitor of the t-test in the univariate setting. For finite dimensional multivariate data, several extensions of the Wilcoxon-Mann-Whitney test have been shown to have better performance than Hotelling's $T^{2}$ test for many non-Gaussian distributions of the data. In this paper, we study a Wilcoxon-Mann-Whitney type test based on spatial ranks for data in infinite dimensional spaces. We demonstrate the performance of this test using some real and simulated datasets. We also investigate the asymptotic properties of the proposed test and compare the test with a wide range of competing tests.