Abstract: We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing non-parametric 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. In particular, one such omnibus test is a circular version of the celebrated distance-covariance test. Thus, we provide a collection of trigonometric-based tests of varying generality and known optimalities. We obtain the large-sample behavior of the tests under the null and alternative hypotheses, and use simulations to show that the new tests are competitive against previous proposals. Lastly, we demonstrate the proposed tests with two data applications in astronomy and forest science.

Key words and phrases: Characteristic function, directional data, independence, trigonometric moments.