On an independence test for polyspherical data and its applications

V. Litvinoff Justus, E. García-Portugués, B. Ebner

An independence test for data on the polysphere, which is defined as the Cartesian product of hyperspheres, is presented. The proposed test statistic is based on the integrated square error of the kernel density estimator for the joint density of the random vectors under the assumption of independence. Under this assumption, the asymptotic distribution of the statistic is derived, which is shown to be normal under conditions similar to the conditions usually employed in kernel density estimation for polyspherical data. A closed form expression for the statistic is derived for the von Mises-Fisher kernel, and a simulation study is conducted to assess the test power under several alternative scenarios. Potential applications of the test are also discussed.

Palabras clave: Directional data; Nonparametric statistics; Independence test; Kernel density estimation; Limit distribution

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4 de septiembre de 2026  15:30
Aula 29

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