Nonparametric tests of independence for circular data based on trigonometric moments

TL;DR

This paper introduces new nonparametric tests for independence in bivariate circular data using trigonometric moments, with optimality properties and broad applicability demonstrated through simulations and real data examples.

Contribution

It proposes locally and asymptotically optimal tests for bivariate circular independence and extends them to omnibus tests using the empirical characteristic function.

Findings

Tests are competitive against existing methods.

Large-sample behaviors are characterized.

Applications in astronomy and forest science demonstrate utility.

Abstract

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.