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

TL;DR

This paper introduces a Wilcoxon-Mann-Whitney type test for infinite dimensional data using spatial ranks, demonstrating its effectiveness through theoretical analysis and empirical evaluation on real and simulated datasets.

Contribution

It extends the Wilcoxon-Mann-Whitney test to infinite dimensional spaces with spatial ranks, providing asymptotic properties and performance comparisons.

Findings

The proposed test performs well on real and simulated datasets.

Asymptotic properties of the test are established.

The test outperforms some existing methods in non-Gaussian settings.

Abstract

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.