Testing multivariate uniformity and its applications

Jia Juan Liang*, Kai Tai Fang, Fred J. Hickernell, Runze Li

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

34 Citations (Scopus)


Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1]d (d ≥ 2). These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in [0, 1]d. Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1]d, we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, N(0, 1), or the chi-squared distribution, χ2(2). A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.

Original languageEnglish
Pages (from-to)337-355
Number of pages19
JournalMathematics of Computation
Issue number233
Early online date17 Feb 2000
Publication statusPublished - Jan 2001
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discrepancy
  • Goodness-of-fit
  • Quasi-Monte Carlo methods
  • Testing uniformity


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