A. Fernández de Marcos Giménez de los Galanes, E. García Portugués
When uniformity on the sphere is tested, most classical tests employ a V-statistic of second order investigating the relation between pairwise observations to detect deviations from uniformity. In this work, we propose two new classes of uniformity tests based on U- and V-statistics of arbitrary order m that capture the interaction between m-tuples of observations. We prove that they extend the well-known Sobolev class of uniformity tests, arising for m=2. Through simulations, we show that tests with m>2 lead to increases in power, compared to m=2, for certain scenarios. The computation of the new class of tests is shown to be manageable even for large m values, and we provide closed-form circular test statistics that extend classical tests for m=2. We study the asymptotic null distribution for these m-tests, its usability in practice, and its asymptotic behavior under local alternatives. In addition, we analyze the effect of m on the rotational invariance of the test statistics.
Palabras clave: Circular data, Spherical data, Uniformity tests
Programado
Estadística no paramétrica: Alta Dimensión
12 de junio de 2025 17:10
Sala de prensa (MR 13)