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

DOI10.1090/S0025-5718-01-01356-4zbMath0985.65004OpenAlexW2057506739MaRDI QIDQ2759098

Hannes Leeb

Publication date: 10 December 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01356-4

zbMATH Keywords

algorithmserror boundslimit distributionequidistribution modulo onediaphonyMonte Carlo sequencesquasi-Monte Carlo sequencesZaremba figure of merit

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Monte Carlo methods (65C05) Signal detection and filtering (aspects of stochastic processes) (60G35) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (3)

Computational aspects of Cui-Freeden statistics for equidistribution on the sphere ⋮ Statistical properties of $b$-adic diaphonies ⋮ Statistical properties of generalized discrepancies

Uses Software

• AS 256

Cites Work

• An extremal problem of Erdős in interpolation theory
• Discrepancy-based error estimates for quasi-Monte Carlo. I: General formalism
• Discrepancy-based error estimates for quasi-Monte Carlo. II: Results in one dimension
• Scrambled net variance for integrals of smooth functions
• Gaussian limits for discrepancies. I: Asymptotic results
• Dyadic diaphony
• Algorithm AS 256: The Distribution of a Quadratic Form in Normal Variables
• Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
• Randomization of Number Theoretic Methods for Multiple Integration
• The weighted spectral test
• A generalized discrepancy and quadrature error bound
• Testing multivariate uniformity and its applications
• Efficient algorithms for computing the $L_2$-discrepancy
• Fourier Analysis of Uniform Random Number Generators
• Convergence of stochastic processes
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