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February, 1983 Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test
Peter J. Bickel, Leo Breiman
Ann. Probab. 11(1): 185-214 (February, 1983). DOI: 10.1214/aop/1176993668

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.

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Peter J. Bickel. Leo Breiman. "Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test." Ann. Probab. 11 (1) 185 - 214, February, 1983. https://doi.org/10.1214/aop/1176993668

Information

Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0502.62045
MathSciNet: MR682809
Digital Object Identifier: 10.1214/aop/1176993668

Subjects:
Primary: 60F05
Secondary: 62G10

Keywords: asymptotics , goodness of fit , Nearest neighbor distances

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 1 • February, 1983
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