A class of k-sample tests for circular data

A. Fernández de Marcos, E. García Portugués

We develop a unified framework for k-sample homogeneity testing on the circle based on Sobolev statistics. The proposed class of k-sample Sobolev tests generalizes the two-sample Sobolev tests based on uniform scores, and encompasses the existing multisample tests as particular cases. Within this class, we introduce the first Anderson–Darling-type homogeneity test for circular data, and we further propose two new tests designed to detect multimodal departures from homogeneity, constructed from Softmax and Poisson kernels. We derive the asymptotic null distribution of the class and prove its consistency against a broad class of fixed alternatives. The tests are distribution-free and therefore do not require resampling. A simulation study shows the Anderson–Darling test is more powerful than the Cramér–von Mises test in various cases, while multimodal tests perform well under suitable alternatives. A zoological dataset illustrates its practical use.

Keywords: Circular data; Multisample tests; Homogeneity tests; Uniform scores; Sobolev tests

GT Estadística no Paramétrica III: Inferencia no paramétrica para datos circulares
September 5, 2026  10:00 AM
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