Some applications of number-theoretic methods in statistics

Kai Tai Fang, Yuan Wang, Peter M. Bentler

Research output: Contribution to journalJournal articlepeer-review

62 Citations (Scopus)

Abstract

Number-theoretic methods (NTM’s) are a class of techniques by which representative points of the uniform distribution on the unit cube of Rs can be generated. NTM have been widely used in numerical analysis, especially in evaluation of high-dimensional integrals. Recently, NTM’s have been extended to generate representative points for many useful multivariate distributions and have been systematically applied in statistics. In this paper, we shall introduce NTM’s and review their applications in statistics, such as evaluation of the expected value of a random vector, statistical inference, regression analysis, geometric probability and experimental design.

Original languageEnglish
Pages (from-to)416-428
Number of pages13
JournalStatistical Science
Volume9
Issue number3
DOIs
Publication statusPublished - Aug 1994
Externally publishedYes

Scopus Subject Areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • F-discrepancy
  • Multivariate distribution
  • Multivariate statistics
  • Number-theoretic method
  • Quasi-monte carlo method

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