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We propose a general and relatively simple method for the construction ofgoodness-of-fit tests on the sphere and the hypersphere. The method is based onthe characterization of probability distributions via their characteristicfunction, and it leads to test criteria that are convenient regardingapplications and consistent against arbitrary deviations from the model undertest. We emphasize goodness-of-fit tests for spherical distributions due totheir importance in applications and the relative scarcity of availablemethods.

A unified approach to goodness-of-fit testing for spherical and hyperspherical data