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Computational Aspects of the Nearest Neighbor Statistics

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Computational Statistics

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Abstract

The distributions of the nearest neighbor statistics and its parameters are calculated in the case when points are generated from the multivariate uniform and multivariate standard normal distribution. A recursive function for the expected value of the k-th nearest neighbor is derived for the asymptotic distributions. Monte Carlo method is used to assess the presented approach.

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References

  1. Clark, P.J. and Evans, F.C. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35. pp. 445–453.

    Article  Google Scholar 

  2. Dziubdziela, W. (1976). A note on the k-th distance random variable. Zastosowania Matematyki 15. pp. 289–291.

    Google Scholar 

  3. Friedman, J. H. and Rafsky, L. C. (1979). Multivariate generalizations of the Wald-Wolfowitz and Smirnov Two-Sample test. The Annals of Statistics 7. pp. 696–717.

    Article  Google Scholar 

  4. Hartigan, JA. (1981). Consistency of single linkage for high-density clusters. Journal of the American Statistical Association 374. pp. 388–394.

    Article  Google Scholar 

  5. Schilling, M.F. (1986). Mutual and shared neighbor probabilities: finite and infinite-dimensional results. Advances in Applied Probability 18. pp. 388–405.

    Article  Google Scholar 

  6. Trybus, E. (1991). An analysis of the minimal spanning tree structure. In Combinatorial Optimization (Ed. Akgul et al.) NATO ASI Series, Vol. F 82, Springer-Verlag, pp. 231-234.

    Google Scholar 

  7. Trybus, E. and Trybus, G. (1985). Distribution of the k-th ordered distance random variable, ASA 1985 Proceedings of the Statistical Computing Section. pp. 332-336.

    Google Scholar 

  8. Trybus, G. (1974). On the distance random variable. Zastosowania Matematyki 14. pp. 237–244.

    Google Scholar 

  9. Trybus G. (1981). The distance random variable: Theory and applications. Prace Naukowe Akademii Ekonomicznej im. O. Langego we Wroclawiu Nr. 173. pp. 1-155.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Management Science, Department of Computer Science, California State University, Northridge, Northridge, CA, 91330, USA

    E. Trybus & G. Trybus

Authors
  1. E. Trybus
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  2. G. Trybus
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Editor information

Editors and Affiliations

  1. Groupe de Statistique, University of Neuchâtel, Pierre-à-Mazel 7, CH-2000, Neuchâtel, Switzerland

    Yadolah Dodge (Professor of Statistics and Operations Research) (Professor of Statistics and Operations Research)

  2. Lancaster University, GB-Lancaster, LA1 4YE, Great Britain

    Joe Whittaker (Professor of Mathematics) (Professor of Mathematics)

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© 1992 Springer-Verlag Berlin Heidelberg

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Trybus, E., Trybus, G. (1992). Computational Aspects of the Nearest Neighbor Statistics. In: Dodge, Y., Whittaker, J. (eds) Computational Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-26811-7_15

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  • DOI: https://doi.org/10.1007/978-3-662-26811-7_15

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-26813-1

  • Online ISBN: 978-3-662-26811-7

  • eBook Packages: Springer Book Archive

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