This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.
Table of Contents
Introduction and number-theoretic method. Numerical evaluation of multiple integral in statistics. Optimization and its applications in statistics. Representative points of a multivariate distribution. Experimental design and design of computer experiments. Statistical inference. Appendices: Tables of glp set. Integrations and uniform distributions on D.
Fang, Kai-Tai; Wang, Y.
"The book offers an interesting opportunity to learn about a particular optimization method applied to a range of statistical problems."
-Short Book Reviews
"...a highly thought provoking book...a valuable addition to the statistical literature."
-Journal of ASA, September 1995
"...this is a book by believers (in the NTM) for believers.
-Journal of RSS