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The almost sure behavior of maximal and minimal multivariate k_n -spacings


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  • Einmahl, J.H.J.

    (Tilburg University)

  • Deheuvels, P.
  • Mason, D.M.
  • Ruymgaart, F.H.


Strong limit theorems are obtained for maximal and minimal multivariate kn-spacings, where {kn}n=1[infinity] is a sequence of positive integers satisfying kn = 0(log n). The shapes, in terms of which these spacings are defined, are allowed to be quite general. They must only satisfy certain "entropy" conditions. The main tool for proving our results is a simple relation between these spacings and empirical measures. A number of examples are also included.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-142048.

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Date of creation: 1988
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Publication status: Published in Journal of Multivariate Analysis (1988) v.24, p.155-176
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-142048

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Cited by:
  1. Claire Coiffard, 2011. "On the Hausdorff dimension of exceptional random sets generated by multivariate spacings," Metrika, Springer, vol. 73(3), pages 359-371, May.
  2. Carando, Daniel & Fraiman, Ricardo & Groisman, Pablo, 2009. "Nonparametric likelihood based estimation for a multivariate Lipschitz density," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 981-992, May.


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