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Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test
Open accessAbstract
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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Citations
Cited by
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Metadata
- Authors
- Bickel, P. J., & Breiman, L.
- Venue
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 1983-02-01
- Volume
- 11
- Issue
- 1
- ISSN
- 0091-1798 (ISSN-L)
- OpenAlex
- W2070276049
- Cited by
- 168
- References
- 0
- FWCI
- 6.17
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test. https://app.cochat.ai/papers/10.1214/aop/1176993668
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- Bickel, P. J., & Breiman, L. (1983). Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test. The Annals of Probability. https://doi.org/10.1214/aop/1176993668
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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