The Annals of Probability

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

Peter J. Bickel and Leo Breiman

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G10: Hypothesis testing

Keywords
Nearest neighbor distances goodness of fit asymptotics

Citation

Bickel, Peter J.; Breiman, Leo. Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test. Ann. Probab. 11 (1983), no. 1, 185--214. doi:10.1214/aop/1176993668. https://projecteuclid.org/euclid.aop/1176993668


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