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Asymptotic properties of the spectral test, diaphony, and related quantities


Author: Hannes Leeb
Journal: Math. Comp. 71 (2002), 297-309
MSC (2000): Primary 65D30, 11K06, 11K45, 60F05, 60G35
DOI: https://doi.org/10.1090/S0025-5718-01-01356-4
Published electronically: August 2, 2001
MathSciNet review: 1863001
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Abstract:

This paper presents the limit laws of discrepancies defined via exponential sums, and algorithms (with error bounds) to approximate the corresponding distribution functions. The results cover the weighted and the nonweighted spectral test of Hellekalek and various instances of the general discrepancies of Hickernell and Hoogland and Kleiss for the exponential function system, as well as classical quantities like the spectral test, diaphony, and the Zaremba figure of merit.


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Additional Information

Hannes Leeb
Affiliation: Department of Statistics, University of Vienna, Universitätsstrasse 5, A-1010 Vienna, Austria
Email: hannes.leeb@univie.ac.at

DOI: https://doi.org/10.1090/S0025-5718-01-01356-4
Keywords: Monte Carlo sequences, quasi-Monte Carlo sequences, equidistribution modulo one, limit distribution
Received by editor(s): September 9, 1999
Received by editor(s) in revised form: May 5, 2000
Published electronically: August 2, 2001
Additional Notes: Research supported by the Austrian Science Foundation (FWF), project no. P11143-MAT
Dedicated: I dedicate the present work to the memory of Hans Stegbuchner
Article copyright: © Copyright 2001 American Mathematical Society

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