Statistical Science

Some Applications of Number-Theoretic Methods in Statistics

Kai-Tai Fang, Yuan Wang, and Peter M. Bentler

Full-text: Open access

Abstract

Number-theoretic methods (NTM's) are a class of techniques by which representative points of the uniform distribution on the unit cube of $R^s$ 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.

Article information

Source
Statist. Sci., Volume 9, Number 3 (1994), 416-428.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177010392

Digital Object Identifier
doi:10.1214/ss/1177010392

Mathematical Reviews number (MathSciNet)
MR1325435

Zentralblatt MATH identifier
0955.62620

JSTOR
links.jstor.org

Keywords
$F$-discrepancy number-theoretic method multivariate distribution multivariate statistics quasi-Monte Carlo method

Citation

Fang, Kai-Tai; Wang, Yuan; Bentler, Peter M. Some Applications of Number-Theoretic Methods in Statistics. Statist. Sci. 9 (1994), no. 3, 416--428. doi:10.1214/ss/1177010392. https://projecteuclid.org/euclid.ss/1177010392


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