P. Navarro Esteban, E. García Portugués, J. A. Cuesta Albertos
We study a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the projected data and the projected uniform distribution. Simple expressions for several test statistics are obtained in particular dimensions. Despite their different origins, the proposed class and the well-studied Sobolev class of uniformity tests are shown to be related. Our new parametrization proves itself advantageous by allowing to derive new tests for hyperspherical data that neatly extend the circular tests by Watson, and Rothman, and by introducing the first instance of an Anderson-Darling-like test in such context. The asymptotic distributions and the local optimality against certain alternatives of the new tests are obtained. A simulation study corroborates the theoretical findings and a real data example illustrates the usage of the new tests.
Keywords: Circular data, directional data, hypersphere, Sobolev tests, uniformity
Scheduled
ENP-1 Non Parametric Statistics
September 4, 2019 2:45 PM
I3L9. Georgina Blanes building