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Some optimal bounds in the central limit theorem using zero biasing


  • Tyurin, I.S.


The convergence rate in the central limit theorem (CLT) is investigated in terms of a wide class of probability metrics. Namely, optimal estimates for the proximity between a probability distribution and its zero bias transformation are derived. These new inequalities allow one to establish optimal rates of convergence in the CLT for sums of independent random variables with finite moments of order s, s∈(2,3], in terms of ideal metrics introduced by V.M. Zolotarev.

Suggested Citation

  • Tyurin, I.S., 2012. "Some optimal bounds in the central limit theorem using zero biasing," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 514-518.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:514-518
    DOI: 10.1016/j.spl.2011.11.010

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    Cited by:

    1. Pinelis, Iosif, 2013. "Exact Rosenthal-type inequalities for p=3, and related results," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2634-2637.

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    CLT; Convergence rate; Zero biasing;


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