A Cramér-von Mises test of uniformity on the hypersphere [article]

Eduardo García-Portugués, Paula Navarro-Esteban, Juan A. Cuesta-Albertos
2021 arXiv   pre-print
Testing uniformity of a sample supported on the hypersphere is one of the first steps when analysing multivariate data for which only the directions (and not the magnitudes) are of interest. In this work, a projection-based Cram\'er-von Mises test of uniformity on the hypersphere is introduced. This test can be regarded as an extension of the well-known Watson test of circular uniformity to the hypersphere. The null asymptotic distribution of the test statistic is obtained and, via numerical
more » ... eriments, shown to be tractable and practical. A novel study on the uniformity of the distribution of craters on Venus illustrates the usage of the test.
arXiv:2008.10767v2 fatcat:3wwnunpnljfvdmly7gpxbfjrwa