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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 View the MathML source for independent random variables ξ1,…,ξn with l zero first odd moments, lgreater-or-equal, slanted1. 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," Scholarly Articles 2624461, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:2624461
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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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