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Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean

Author

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  • Marc Kesseböhmer

    (Universität Bremen)

  • Tanja Schindler

    (Australian National University)

Abstract

We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.

Suggested Citation

  • Marc Kesseböhmer & Tanja Schindler, 2019. "Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean," Journal of Theoretical Probability, Springer, vol. 32(2), pages 702-720, June.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-017-0802-0
    DOI: 10.1007/s10959-017-0802-0
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    References listed on IDEAS

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    1. Einmahl, J.H.J. & Haeusler, E. & Mason, D.M., 1988. "On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics," Other publications TiSEM df0f63ff-d20e-4578-86ae-8, Tilburg University, School of Economics and Management.
    2. Csörgo, Sándor & Simons, Gordon, 1996. "A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 65-73, January.
    3. Aaronson, Jon & Nakada, Hitoshi, 2003. "Trimmed sums for non-negative, mixing stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 173-192, April.
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