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\'{ e}r 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.
Categories: math.ST stat.TH