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.

翻译：本文提出了一种基于球极投影的(超)球面数据均匀性检验方法。利用Gegenbauer多项式推导了检验统计量的闭式表达式及其零假设下的渐近分布。给出了针对旋转对称局部备择假设的功效分析，并通过仿真验证了非零假设下的渐近结果。在具有对映依赖性的检验场景中，球极投影检验方法优于其他检验方法。