Summary
Two-sided bounds are derived for nonuniform rates of convergence in the central limit theorem, and are applied to solve several problems on rates of convergence in nonuniform metrics. In particular, an expression for the fastest rate of convergence is obtained, and rates of convergence using different norming constants are compared. A useful estimate of the rate of convergence in the (1+¦x¦2+ɛ)-metric is derived, which does not require the assumption of (2+ɛ)'th order moments.
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Hall, P. Two-sided bounds for nonuniform rates of convergence in the central limit theorem. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 61–72 (1983). https://doi.org/10.1007/BF00534994
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DOI: https://doi.org/10.1007/BF00534994