Normalization of the Spectral Test in High Dimensions

Entacher Karl, Laimer Gerold, Röck Harald and Uhl Andreas
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Entacher Karl: School of Telecommunications Engineering, Salzburg Univ. of Applied Sciences and Technology
Laimer Gerold: Department of Scientific Computing, Salzburg University, AUSTRIA
Röck Harald: Department of Scientific Computing, Salzburg University, AUSTRIA
Uhl Andreas: Department of Scientific Computing, Salzburg University, AUSTRIA

Monte Carlo Methods and Applications, 2004, vol. 10, issue 3-4, 265-274

Abstract: The spectral test provides a reliable measure for lattice assessment and can be computed very efficiently. It has extensively been applied to find good lattices for several MC and QMC applications. In order to enable comparisons across dimensions, a normalized spectral test is widely used. We empirically demonstrate significant shortcomings of this normalization in high dimensions, discuss the empirical distribution of the normalized spectral test values, and propose a new normalization strategy. The new normalization is shown to give more reliable results, especially concerning the comparability of the values accross dimensions.

Keywords: Monte Carlo Simulation; pseudo-random numbers; LCG; spectral test; parameter search; lattice rules; quasi Monte Carlo Methods (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1515/mcma.2004.10.3-4.265

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