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Optimal constants in the Rosenthal inequality for random variables with zero odd moments

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  • Ibragimov, Marat
  • Ibragimov, Rustam

Abstract

We obtain estimates for the best constant in the Rosenthal inequality for independent random variables [xi]1,...,[xi]n with l zero first odd moments, l[greater-or-equal, slanted]1. The estimates are sharp in the extremal cases l=1 and l=m, that is, in the cases of random variables with zero mean and random variables with m zero first odd moments.

Suggested Citation

  • Ibragimov, Marat & Ibragimov, Rustam, 2008. "Optimal constants in the Rosenthal inequality for random variables with zero odd moments," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 186-189, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:186-189
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    1. Ibragimov, R. & Sharakhmetov, Sh., 2001. "The best constant in the Rosenthal inequality for nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 367-376, December.
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