Nonparametric Tests of Independence for Circular Data Based on Trigonometric Moments
Eduardo García‐Portugués, Pierre Lafaye de Micheaux, Simos G. Meintanis, Thomas Verdebout · Statistica Sinica · 2022
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 alter-Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) natives, eventually being omnibus.In particular, one of such omnibus tests is a circular version of the celebrated distance-covariance test.We thus provide a collection of trigonometric-based tests of varying generality and known optimalities.The large-sample behavior 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.