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

We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function, and it leads to test criteria that are convenient regarding applications and consistent against arbitrary deviations from the model under test. We emphasize goodness-of-fit tests for spherical distributions due to their importance in applications and the relative scarcity of available methods.