Some optimal bounds in the central limit theorem using zero biasing

I.S. Tyurin

Statistics & Probability Letters, 2012, vol. 82, issue 3, 514-518

Abstract: 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.

Keywords: CLT; Convergence rate; Zero biasing (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2011.11.010

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