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Statistical Distances Based on Euclidean Graphs

In: Recent Advances in Applied Probability

Author

Listed:
  • R. Jiménez

    (Universidad Simón Bolívar, Departamento de Estadística)

  • J. E. Yukich

    (Lehigh University, Department of Mathematics)

Abstract

A general approach, based on covering by cells, induced by Euclidean graphs, is developed to provide asymptotic characterizations of multivariate sample densities. This approach provides high dimensional analogs of basic results for random partitions based on one-dimensional sample spacings. The methods used in the proofs yield asymptotics for empirical φ-divergences based on k-spacings and also for the total edge length of the graphs involved.

Suggested Citation

  • R. Jiménez & J. E. Yukich, 2005. "Statistical Distances Based on Euclidean Graphs," Springer Books, in: Ricardo Baeza-Yates & Joseph Glaz & Henryk Gzyl & Jürgen Hüsler & José Luis Palacios (ed.), Recent Advances in Applied Probability, pages 223-239, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-23394-9_10
    DOI: 10.1007/0-387-23394-6_10
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