Functional K Sample Problem via Multivariate Optimal Measure Transport-Based Permutation Test
Abstract
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 Cram\'er 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.
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