Title: Optimal testing for symmetry on the torus Authors:  Sophia Loizidou - University of Luxembourg (Luxembourg) [presenting]
Andreas Anastasiou - University of Cyprus (Cyprus)
Christophe Ley - University of Luxembourg (Luxembourg)
Abstract: Several complex real-world data can be viewed as points on the hyper-torus, which is the cartesian product of circles. Over the past few years, this has motivated 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. A new semi-parametric test is presented, a test which is valid not only under a given parametric hypothesis but also under a very broad class of symmetric distributions. A description of its construction and 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 behavior (through Monte Carlo simulations) will be given, as well as an application of the test on protein data.