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Title: Optimal tests for circular reflective symmetry Authors:  Christophe Ley - Ghent University (Belgium) [presenting]
Jose Ameijeiras-Alonso - KU Leuven (Belgium)
Arthur Pewsey - University of Extremadura (Spain)
Thomas Verdebout - Universite Libre de Bruxelles (Belgium)
Abstract: Parametric and semiparametric tests of circular reflective symmetry about an unknown central direction are developed that are locally and asymptotically optimal in the Le Cam sense against asymmetric k-sine-skewed distributions. Our findings shed new light on and unify existing results on the same topic, providing inter alia the popular Pewsey test of symmetry with so far unknown efficiency properties. The results from Monte Carlo studies comparing the rejection rates of the tests with those of previously proposed tests lead to recommendations regarding the use of the various tests with small- to medium-sized samples. Analyses of data on the directions of cracks in cemented femoral components and the times of gun crimes in Pittsburgh illustrate the proposed methodology.