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A universal law of the iterated logarithm for trimmed and censored sums

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Probability Theory on Vector Spaces IV

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1391))

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Abstract

The conditionally trimmed (resp. censored) sums formed from an arbitrary i.i.d. sample are shown to satisfy a universal law of the iterated logarithm (LIL). The specific method of trimming (resp. censoring) attempts to retain as many summands as possible, and trims (resp. censors) only terms of sufficient magnitude.

Supported in part by NSF grant DMS-87-02878

Supported in part by NSF grant DMS-85-21586

Supported in part by NSF grant DMS-86-03188.

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References

  1. Feller, W. (1968). An introduction to probability theory and its applications: vol. I, third edition. John Wiley & Sons, New York.

    MATH  Google Scholar 

  2. Griffin, P. S. (1985). Laws of the iterated logarithm for symmetric stable processes. Z. Wahrsch. verw. Gebiete, 68, 271–285.

    Article  MathSciNet  MATH  Google Scholar 

  3. Griffin, P. S. (1985). The influence of extremes on the law of the iterated logarithm. Preprint.

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  4. Hahn, M. G. and Kuelbs, J. (1987). Universal Asymptotic Normality for Trimmed Sums. Preprint.

    Google Scholar 

  5. Hahn, M. G., Kuelbs, J. and Weiner, D. C. (1987), Joint estimation of some center and scale parameters via self-normalization for distributions with possibly infinite mean and variance, Preprint.

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  6. Kuelbs, J. (1977). Kolmogorov's law of the iterated logarithm for Banach space valued random variables. Illinois J. 21, 784–800.

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  7. Kuelbs, J. and Ledoux, M. (1985). Extreme values and LIL behavior. Preprint.

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  8. Stout, W. F. (1974). Almost sure convergence, Academic Press, New York.

    MATH  Google Scholar 

  9. Weiner, D. C. (1986), Centrality, scale, and asymptotic normality for sums of independent random variables, Preprint.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tufts University, 02155, Medford, MA, U.S.A.

    M. G. Hahn

  2. Department of Mathematics, University of Wisoonsin, 213 Van Vleck Hall, 53706, Madison, WI, U.S.A.

    J. Kuelbs

  3. Department of Mathematics, Boston University, 02215, Boston, MA, U.S.A.

    D. C. Weiner

Authors
  1. M. G. Hahn
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  2. J. Kuelbs
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  3. D. C. Weiner
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Editor information

Stamatis Cambanis Aleksander Weron

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© 1989 Springer-Verlag

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Hahn, M.G., Kuelbs, J., Weiner, D.C. (1989). A universal law of the iterated logarithm for trimmed and censored sums. In: Cambanis, S., Weron, A. (eds) Probability Theory on Vector Spaces IV. Lecture Notes in Mathematics, vol 1391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083383

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  • DOI: https://doi.org/10.1007/BFb0083383

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51548-7

  • Online ISBN: 978-3-540-48244-4

  • eBook Packages: Springer Book Archive

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