Abstract

Several complex data in the real world can be viewed as data on the hyper-torus, which is the cartesian product of circles. This has motivated, over the past years, new proposals of distributions on the torus, both (pointwise) symmetric and sine-skewed asymmetric. In practice, it is relevant to know whether one should use the simpler symmetric models or the more convoluted yet more general asymmetric ones. So far, only parametric likelihood ratio tests have been defined to distinguish between a symmetric density and its sine-skewed counterpart. In this talk, a new semi-parametric test is presented, a test which is not only valid under a given parametric hypothesis but instead under a very broad class of symmetric distributions. A description of its construction, asymptotic properties under the null and alternative hypotheses will be presented. Using Stein's method, bounds for the rate of convergence of the test statistic are derived and finite sample behaviour (through Monte Carlo simulations) will be given, as well as an application of the test on protein data.