2025/10/21 by Lujia Bai, Holger Dette, Bai, Lujia +1
Mathematics · #Random Matrices and Applications #Statistical Methods and Inference #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2510.18598
Most of the work on checking spherical symmetry assumptions on the distribution of the p-dimensional random vector Y has its focus on statistical tests for the null hypothesis of exact spherical symmetry. In this paper, we take a different point of view and propose a measure for the deviation from spherical symmetry, which is based on the minimum distance between the distribution of the vector (‖Y‖, Y/ ‖Y‖ )^\top and its best approximation by a distribution of a vector (‖Ys‖, Ys/ ‖Ys ‖ )^\top corresponding to a random vector Ys with a spherical distribution. We develop estimators for the minimum distance with corresponding statistical guarantees (provided by asymptotic theory) and demonstrate the applicability of our approach by means of a simulation study and a real data example.