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 experiments, 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.

翻译：在分析多变量数据时,在超视镜上支持的样本的统一性测试是第一步之一,分析这些数据时,只有方向(而不是数量)才有意义。在这项工作中,采用了基于投射的Cram\'er-von Mises 测试,对超视镜进行了统一性测试。这一测试可被视为著名的Watson测试,将圆形统一的测试扩展至超视镜。获得测试统计数据的无症状分布,通过数字实验显示,测试统计数据的可移植性和实用性。关于金星上弹坑分布的统一性的新研究展示了测试的使用情况。