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On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics
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  • Published: September 1988

On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics

  • J. H. J. Einmahl1,
  • E. Haeusler2 &
  • D. M. Mason3 

Probability Theory and Related Fields volume 79, pages 59–74 (1988)Cite this article

Summary

We shall disclose a relationship between the almost sure stability of weighted empirical distribution functions and sums of order statistics. First we obtain an extension of a theorem due to Csáki on the almost sure stability of the standardized uniform empirical distribution function. This result is then shown to be an essential tool to derive a characterization of the almost sure stability of the sum of k nupper order statistics from a sample of n independent observations from a distribution with positive support in the domain of attraction of a non-normal stable law, where 1≦k n≦n and k n→∞ as n→∞.

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References

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Author information

Authors and Affiliations

  1. Department of Medical Informatics and Statistics, University of Limburg, P.O. Box 616, 6200 MD, Maastricht, The Netherlands

    J. H. J. Einmahl

  2. Mathematisches Institut der Universität München, Theresienstrasse 39, D-8000, München 2, Federal Republic of Germany

    E. Haeusler

  3. Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA

    D. M. Mason

Authors
  1. J. H. J. Einmahl
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  2. E. Haeusler
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  3. D. M. Mason
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Additional information

Research performed while the author was at the Catholic University Nijmegen

Research supported by the Alexander von Humboldt Foundation while the author was visiting the University of Munich on leave from the University of Delaware

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Cite this article

Einmahl, J.H.J., Haeusler, E. & Mason, D.M. On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics. Probab. Th. Rel. Fields 79, 59–74 (1988). https://doi.org/10.1007/BF00319104

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  • Received: 10 October 1985

  • Revised: 17 February 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319104

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Keywords

  • Distribution Function
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Order Statistic
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