Although there have been fairly recent advances regarding inference for three-dimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3-D rotations. In this paper, nonparametric inference is used to test if F 1=F 2, where F i is the degree of rotational symmetry of distribution i, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics.

中文翻译：

---

用于比较三维旋转数据集中旋转对称性的置换测试

尽管关于三维旋转数据的推断已经有了相当新的进展，但是仍然有许多有趣的领域有待探索。其中一个领域涉及比较3D旋转的旋转对称性。在本文中，通过置换检验，使用非参数推断来检验F 1 = F 2，其中F i是分布i的旋转对称度。通过模拟研究检查了开发的置换测试的有效性，并将该测试应用于生物力学中的一个小例子。