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

Author

Listed:
  • Deheuvels, Paul
  • Einmahl, John H. J.
  • Mason, David M.
  • Ruymgaart, Frits H.

Abstract

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.

Suggested Citation

  • Deheuvels, Paul & Einmahl, John H. J. & Mason, David M. & Ruymgaart, Frits H., 1988. "The almost sure behavior of maximal and minimal multivariate kn-spacings," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 155-176, January.
    • Handle: RePEc:eee:jmvana:v:24:y:1988:i:1:p:155-176
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    Cited by:

    1. Claire Coiffard, 2011. "On the Hausdorff dimension of exceptional random sets generated by multivariate spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 359-371, May.
    2. Major, Péter, 2016. "Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 118-137.
    3. 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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