sphunif-package {sphunif}

sphunif: Uniformity Tests on the Circle, Sphere, and Hypersphere

Description

Implementation of uniformity tests on the circle and (hyper)sphere. The main function of the package is unif_test, which conveniently collects more than 35 tests for assessing uniformity on S^{p-1}=\{{\bf x}\in R^p:||{\bf x}||=1\}, p\ge 2. The test statistics are implemented in the unif_stat function, which allows computing several statistics for different samples within a single call, thus facilitating Monte Carlo experiments. Furthermore, the unif_stat_MC function allows parallelizing them in a simple way. The asymptotic null distributions of the statistics are available through the function unif_stat_distr. The core of sphunif-package is coded in C++ by relying on the Rcpp-package. The package also provides several novel datasets and gives the replicability for the data applications/ simulations in García-Portugués et al. (2021) <doi:10.1007/978-3-030-69944-4_12>, García-Portugués et al. (2023) <doi:10.3150/21-BEJ1454>, García-Portugués et al. (2024) <doi:10.48550/arXiv.2108.09874>, and Fernández-de-Marcos and García-Portugués (2024) <doi:10.48550/arXiv.405.13531>.

Author(s)

Eduardo García-Portugués and Thomas Verdebout.

References

Fernández-de-Marcos, A. and García-Portugués, E. (2024) A stereographic test of spherical uniformity. arXiv:2405.13531. doi:10.48550/arXiv.2405.13531.

García-Portugués, E. and Verdebout, T. (2018) An overview of uniformity tests on the hypersphere. arXiv:1804.00286. doi:10.48550/arXiv.1804.00286.

García-Portugués, E., Navarro-Esteban, P., Cuesta-Albertos, J. A. (2023) On a projection-based class of uniformity tests on the hypersphere. Bernoulli, 29(1):181–204. doi:10.3150/21-BEJ1454.

García-Portugués, E., Navarro-Esteban, P., and Cuesta-Albertos, J. A. (2021). A Cramér–von Mises test of uniformity on the hypersphere. In Balzano, S., Porzio, G. C., Salvatore, R., Vistocco, D., and Vichi, M. (Eds.), Statistical Learning and Modeling in Data Analysis, Studies in Classification, Data Analysis and Knowledge Organization, pp. 107–116. Springer, Cham. doi:10.1007/978-3-030-69944-4_12.

García-Portugués, E., Paindaveine, D., and Verdebout, T. (2024). On a class of Sobolev tests for symmetry of directions, their detection thresholds, and asymptotic powers. arXiv:2108.09874v2. doi:10.48550/arXiv.2108.09874.