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.

翻译：我们提出了一种通用且相对简单的方法，用于在球面和超球面上构建拟合优度检验。该方法基于通过特征函数对概率分布进行刻画，所得到的检验准则在实际应用中具有便利性，并且能一致地检测出与待检验模型的任意偏差。我们重点讨论了球面分布的拟合优度检验，这是因为它们在应用中具有重要意义，且现有方法相对匮乏。