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Refined Baum-Katz laws for weighted sums of iid random variables

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  • Lanzinger, H.
  • Stadtmüller, U.

Abstract

We consider weighted sums with iid random variables (Xn) and compare the tail probabilities of these sums with the moment conditions on X1. If X1 is in the domain of attraction of a stable law then refined Baum-Katz laws generalizing results of Heyde, Gut and other authors are presented. Some special examples of weights pnk originating from summability are discussed.

Suggested Citation

  • Lanzinger, H. & Stadtmüller, U., 2004. "Refined Baum-Katz laws for weighted sums of iid random variables," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 357-368, September.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:357-368
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    References listed on IDEAS

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    1. Liang, Han-Ying, 2000. "Complete convergence for weighted sums of negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 317-325, July.
    2. Liang, Han-Ying & Su, Chun, 1999. "Complete convergence for weighted sums of NA sequences," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 85-95, October.
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    Cited by:

    1. Fa-mei Zheng & Qing-pei Zang, 2015. "A general pattern of asymptotic behavior of the R/S statistics for linear processes," Statistical Papers, Springer, vol. 56(1), pages 191-204, February.

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