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.

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

SERI, RAFFAELLO
2013-01-01

Abstract

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.
2013
http://dx.doi.org/10.1090/S0025-5718-2013-02698-1
Sphere; Generalized discrepancy; Equidistribution; Approximation of distributions; Quadratic forms in Gaussian random variables; Low discrepancy (quasi-Monte Carlo) method
Choirat, C.; Seri, Raffaello
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1746350
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