Omnibus Goodness-of-Fit Testing for Distributions on Stiefel Manifolds

作者：Dominic Edelmann, Donald Richards · 发表于：arXiv (Cornell University) · 年份：2026 · 研究领域：Random Matrices and Applications、Bayesian Methods and Mixture Models、Statistical Methods and Inference

In this article, a comprehensive framework for goodness-of-fit testing for distributions on Stiefel manifolds is developed. The approach is based on integrals of the squared differences between empirical and theoretical characteristic functions, yielding test statistics that are consistent against all fixed alternatives. For the Fisher-Bingham family of distributions, explicit computable forms of the test statistic are derived. Simplified expressions for important special cases, including the matrix Fisher, matrix Bingham, and uniform distributions are provided. In the case of testing uniformity on hyperspheres, we obtain the complete asymptotic distribution of the test statistic, enabling computationally efficient asymptotic testing. For general Fisher-Bingham distributions, we establish theoretically justified Monte Carlo testing procedures for both simple and composite hypotheses. Simulation studies demonstrate accurate Type I error control and strong power across a wide range of alternatives. The practical relevance of the proposed methodology is illustrated by an application to data on the orbits of comets.