Testing multivariate uniformity and its applications

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

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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 (US)
Pages (from-to)337-355
Number of pages19
JournalMathematics of Computation
Volume70
Issue number233
StatePublished - Jan 2001

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Uniformity
Statistics
Testing
Quasi-Monte Carlo Methods
Chi-squared distribution
Standard Normal distribution
Unit cube
Normal distribution
Goodness of fit
Uniform distribution
Null hypothesis
Identically distributed
Asymptotic Properties
Discrepancy
Monte Carlo methods
Monte Carlo Simulation

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics
  • Computational Mathematics

Cite this

Liang, J. J., Fang, K. T., Hickernell, F. J., & Li, R. (2001). Testing multivariate uniformity and its applications. Mathematics of Computation, 70(233), 337-355.
Liang, Jia Juan ; Fang, Kai Tai ; Hickernell, Fred J. ; Li, Runze. / Testing multivariate uniformity and its applications. In: Mathematics of Computation. 2001 ; Vol. 70, No. 233. pp. 337-355.
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Liang, JJ, Fang, KT, Hickernell, FJ & Li, R 2001, 'Testing multivariate uniformity and its applications', Mathematics of Computation, vol. 70, no. 233, pp. 337-355.

Testing multivariate uniformity and its applications. / Liang, Jia Juan; Fang, Kai Tai; Hickernell, Fred J.; Li, Runze.

In: Mathematics of Computation, Vol. 70, No. 233, 01.2001, p. 337-355.

Research output: Contribution to journalArticle

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Liang JJ, Fang KT, Hickernell FJ, Li R. Testing multivariate uniformity and its applications. Mathematics of Computation. 2001 Jan;70(233):337-355.