球面均匀性的立体测试

Pub Date : 2024-07-24 DOI:10.1016/j.spl.2024.110218

Alberto Fernández-de-Marcos, Eduardo García-Portugués

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引用次数: 0

摘要

我们在立体投影的基础上引入了（超）球面数据的均匀性检验。利用格根鲍尔多项式导出了检验统计量的闭式表达式及其空渐近分布。提供了针对旋转对称局部替代方案的功率，并通过模拟说明了非空渐近结果。在观测值之间存在反向依赖关系的测试场景中，立体检验优于其他检验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A stereographic test of spherical uniformity

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.

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