Centered L2-discrepancy of random sampling and latin hypercube design, and construction of uniform designs

Kai Tai Fang*, Chang Xing Ma, Peter Winker

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

160 Citations (Scopus)

Abstract

In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

Original languageEnglish
Pages (from-to)275-296
Number of pages22
JournalMathematics of Computation
Volume71
Issue number237
Early online date16 Oct 2000
DOIs
Publication statusPublished - 2002
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Latin hypercube design
  • Quasi-Monte Carlo methods
  • Threshold accepting heuristic
  • Uniform design

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