The Annals of Probability

Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test

Abstract

We study the limiting behavior of sums of functions of nearest neighbor distances for an $m$ dimensional sample. We establish a central limit theorem and moment bounds for such sums and an invariance principle for the empirical process of nearest neighbor distances. As a consequence we obtain the asymptotic behavior of a practicable goodness of fit test based on nearest neighbor distances.

Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 185-214.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993668

Digital Object Identifier
doi:10.1214/aop/1176993668

Mathematical Reviews number (MathSciNet)
MR682809

Zentralblatt MATH identifier
0502.62045

JSTOR