Multivariate optimal-transport based permutation tests

This is an illustration of usage of multivariate permutation tests based on optimal measure transport (so called multivariate OT permutation tests), proposed by

• Hlávka, Z., Hlubinka, D., & Hudecová, Š. (2025). Multivariate quantile-based permutation tests with application to functional data. Journal of Computational and Graphical Statistics, 1-15.

The following topics and examples are provided on separate pages:

• Various approaches to the construction of a grid set.
• An example of a permutation test for a two-sided bivariate test statistic.
• An example for a permutation test for a two-sided trivariate test statistic.
• An application to the functional data from Section 6 of the above paper. This example serves also as an illustration of a permutation test for a bivariate one-sided test statistics.

Furthermore, we provide also an example of an application of the functional \(K\)-sample test based on characteristic functions to Bitcoin data.

• Hudecová, Š., Hlubinka, D., & Hlávka, Z. (2025). Functional K Sample Problem via Multivariate Optimal Measure Transport-Based Permutation Test. In International Workshop on Functional and Operatorial Statistics (pp. 249-257). Springer, Cham. An ArXiv version .

All outputs were obtained in R version 4.4.1 (2024-06-14).