Testing for bivariate spherical symmetry

An omnibus test for spherical symmetry in a"e(2) is proposed, employing localized empirical likelihood. The thus obtained test statistic is distribution free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good performance of the test is demonstrated. Furthermore, a real data example is presented.