Computational Aspects of Cui-Freeden Statistics for Equidistribution on the Sphere


In this paper, we derive the asymptotic statistical properties of a class of generalized discrepancies introduced by Cui and Freeden (SIAM J. Sci. Comput., 1997) to test equidistribution on the sphere. We show that they have highly desirable properties and encompass several statistics already proposed in the literature. In particular, it turns out that the limiting distribution is an (infinite) weighted sum of chi-squared random variables. Issues concerning the approximation of this distribution are considered in detail and explicit bounds for the approximation error are given. The statistics are then applied to assess the equidistribution of Hammersley low discrepancy sequences on the sphere and the uniformity of a dataset concerning magnetic orientations.

Mathematics of Computation, 82(284), 2137-2156

Raffaello Seri
Raffaello Seri
Professor of Econometrics

My research interests include statistics, numerical analysis, operations research, psychology, economics and management.