DMCA
Close-point spatial tests and their application to random number generators (1997)
| Venue: | Operations Research |
| Citations: | 10 - 5 self |
BibTeX
@ARTICLE{Cordeau97close-pointspatial,
author = {Jean-françois Cordeau and Richard Simard},
title = {Close-point spatial tests and their application to random number generators},
journal = {Operations Research},
year = {1997},
volume = {48},
pages = {308--317}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We study statistical tests of uniformity based on the L p-distances between the m nearest pairs of points, for n points generated uniformly over the k-dimensional unit hypercube or unit torus. The number of distinct pairs at distance no more than t, for t � 0, is a stochastic process whose initial part, after an appropriate transformation and as n3�, is asymptotically a Poisson process with unit rate. Convergence to this asymptotic is slow in the hypercube as soon as k exceeds 2 or 3, due to edge effects, but is reasonably fast in the torus. We look at the quality of approximation of the exact distributions of the tests statistics by their asymptotic distributions, discuss computational issues, and apply the tests to random number generators. Linear congruential generators fail decisively certain variants of the tests as soon as n approaches the square root of the period length. Multidimensional goodness-of-fit tests based on nearest-neighbor distances have been proposed and studied in the statistical literature; see Bickel and Breiman (1983), Cressie (1993), Ripley (1977, 1988), and other references therein. Given a set of points in space, these tests seek evidence against the hypothesis that the points are an i.i.d. sample from a specified multivariate distribution. They are based, for example, on the distance separating
Keyphrases
number generator close-point spatial test test statistic poisson process unit torus distinct pair nearest-neighbor distance appropriate transformation discus computational issue distance separating specified multivariate distribution k-dimensional unit hypercube multidimensional goodness-of-fit test statistical test statistical literature period length asymptotic distribution initial part square root stochastic process exact distribution unit rate certain variant linear congruential generator
