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Berry-Esseen-type inequality for a special class of distributions

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Abstract

LetQ be the distribution of the suitably normalized sum of i. i. d.k-dimensional random vectors (k≥2) and letf be a measurable real valued function of the formf(z 1,...,z k )=z 1+r(z 2,...,z k ), where the measurable functionr fulfills certain regularity conditions. A Berry-Esseen-type inequality is derived for the one-dimensional distributionP=Qf −1.

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  1. Institut für mathematische Stochastik der Universität Hamburg, Rothenbaumchaussee 45, D-2000, Hamburg 13

    M. Schaefer

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  1. M. Schaefer
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Schaefer, M. Berry-Esseen-type inequality for a special class of distributions. Metrika 22, 77–83 (1975). https://doi.org/10.1007/BF01899717

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  • DOI: https://doi.org/10.1007/BF01899717

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