In this paper, we study the asymptotic statistical properties of some discrepancies defined on the unit hypercube, originally introduced in Numerical Analysis to assess the equidistribution of low-discrepancy sequences. We show that they have highly desirable properties. Nevertheless, it turns out that the limiting distribution is an (infinite) weighted sum of chi-squared random variables. This raises some problems concerning the approximation of the asymptotic distribution. These issues are considered in detail: several solutions are proposed and compared, and bounds for the approximation error are discussed.

Computational aspects of discrepancies for equidistribution on the hypercube

SERI, RAFFAELLO
2012-01-01

Abstract

In this paper, we study the asymptotic statistical properties of some discrepancies defined on the unit hypercube, originally introduced in Numerical Analysis to assess the equidistribution of low-discrepancy sequences. We show that they have highly desirable properties. Nevertheless, it turns out that the limiting distribution is an (infinite) weighted sum of chi-squared random variables. This raises some problems concerning the approximation of the asymptotic distribution. These issues are considered in detail: several solutions are proposed and compared, and bounds for the approximation error are discussed.
2012
The International Statistical Institute/International Association for Statistical Computing
9789073592322
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1756953
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