Permutation Testing for Equality Across Functional Data Samples

Summary

This paper addresses whether functional observations from K samples share the same distribution. It builds a multivariate test statistic from pairwise Cramér–von Mises comparisons of empirical characteristic functionals, allowing the test to assess distributional equality across the groups.

To combine the component comparisons into one significance measure, the method uses a multivariate permutation procedure and discrete optimal measure transport to compute a single p-value. The stated illustration uses cumulative intraday Bitcoin returns. The document gives no numerical findings, design details, or comparison with alternative tests, so it establishes the method's outline but not how its performance varies with sample size, dependence, or other data conditions.

Key ideas

• The null hypothesis is equality of distributions across multiple functional data samples.
• Pairwise Cramér–von Mises comparisons of empirical characteristic functionals form the multivariate statistic.
• A permutation procedure evaluates significance and produces a single p-value through discrete optimal measure transport.
• Cumulative intraday Bitcoin returns provide the real-data illustration.

Tags

# Functional $K$ Sample Problem via Multivariate Optimal Measure Transport-Based Permutation Test


# Functional $K$ Sample Problem via Multivariate Optimal Measure Transport-Based Permutation Test









The null hypothesis of equality of distributions of functional data coming from $K$ samples is considered. The proposed test statistic is multivariate and its components are based on pairwise Cramér von Mises comparisons of empirical characteristic functionals. The significance of the test statistic is evaluated via the novel multivariate permutation test, where the final single $p$-value is computed using the discrete optimal measure transport. The methodology is illustrated by real data on cumulative intraday returns of Bitcoin.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.