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A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games

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  • Csörgo, Sándor
  • Simons, Gordon

Abstract

Extending a result of Einmahl, Haeusler and Mason (1988), a characterization of the almost sure asymptotic stability of lightly trimmed sums of upper order statistics is given when the right tail of the underlying distribution with positive support is surrounded by tails that are regularly varying with the same index. The result is motivated by applications to cumulative gains in a sequence of generalized St. Petersburg games in which a fixed number of the largest gains of the player may be withheld.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:1:p:65-73
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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.
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    Cited by:

    1. David M. Mason, 2006. "Cluster Sets of Self-Normalized Sums," Journal of Theoretical Probability, Springer, vol. 19(4), pages 911-930, December.
    2. Csörgo, Sándor & Simons, Gordon, 2007. "St. Petersburg games with the largest gains withheld," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1185-1189, July.
    3. 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.
    4. Vu T. N. Anh & Nguyen T. T. Hien & Le V. Thanh & Vo T. H. Van, 2021. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 34(1), pages 331-348, March.
    5. Kevei, Péter, 2007. "Generalized n-Paul paradox," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1043-1049, June.
    6. Allan Gut & Anders Martin-Löf, 2016. "A Maxtrimmed St. Petersburg Game," Journal of Theoretical Probability, Springer, vol. 29(1), pages 277-291, March.
    7. Alina Bazarova & István Berkes & Lajos Horváth, 2016. "On the Extremal Theory of Continued Fractions," Journal of Theoretical Probability, Springer, vol. 29(1), pages 248-266, March.
    8. István Berkes & László Györfi & Péter Kevei, 2017. "Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1104-1129, September.
    9. Gut, Allan & Martin-Löf, Anders, 2015. "Extreme-trimmed St. Petersburg games," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 341-345.

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    1. 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.

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