A stereographic test of spherical uniformity
arXiv:2405.13531 · doi:10.1016/j.spl.2024.110218
Abstract
We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.
12 pages, 5 figures, 1 table