We propose a general and relatively simple method to construct 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.

中文翻译：

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球形和超球形数据拟合优度测试的统一方法

我们提出了一种通用且相对简单的方法来构建球体和超球体的拟合优度检验。该方法基于通过特征函数来表征概率分布，并且它导致测试标准在应用方面很方便，并且与被测模型的任意偏差保持一致。我们强调球形分布的拟合优度检验，因为它们在应用中很重要，而且可用方法相对稀缺。