We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing nonparametric tests that are locally and asymptotically optimal against bivariate cosine von Mises alternatives and (ii) extending these tests, via the empirical characteristic function, to obtain consistent tests against broader sets of alternatives, eventually being omnibus. We thus provide a collection of trigonometric-based tests of varying generality and known optimalities. The large-sample behaviours of the tests under the null and alternative hypotheses are obtained, while simulations show that the new tests are competitive against previous proposals. Two data applications in astronomy and forest science illustrate the usage of the tests.

翻译：我们对基于三角数时的双轨循环数据进行非对称独立测试,我们的贡献在于:(一) 提议对双轨 Cosine von Misses 替代品进行当地和无症状最佳的非对称测试,(二) 通过经验特征功能扩大这些测试,以获得对更广泛的替代品的一致测试,最终是总括的,因此我们提供了一系列基于三角的、具有不同普遍性和已知最佳性的测试,在无效假设和替代假设下进行了大量抽样测试,而模拟则表明新测试与以前的提案相比具有竞争力。天文学和森林科学中的两种数据应用说明了测试的使用情况。