球面均匀分布的拟合优度检验

Goodness-of-fit Analysis for Uniformity on the Surface of a Unit Sphere

证明了基于惯量矩的d维单位球面上样本服从均匀分布的基本特征,得到球面均匀分布协差阵特征根估计的强相合性及渐近多元正态性.提出了检验球面上样本均匀性的渐近卡方统计量,证明了拟合优度检验的相合性并做检验功效的随机模拟.

Based on the moment of inertia of the samples on the surface of a unit sphere, the basic characterzation of d-dimentional samples with a uniform distribution on the surface of a unit sphere is proved, the strong consistency and asymptotic multinormality of the centroid and the eigenvalue estimators of the covariance matrix of the unit sphere uniform distribution are obtained, the asymptotic Chi squared statistic for testing uniformity of a given sample on the surface of a unit sphere is suggested. The consistency of the goodnessof-fit tests is proved and the empirical power of tests is made.