Some Applications of Number-Theoretic Methods in Statistics

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.