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arXiv · 1212.5401

On rates of convergence and Berry-Esseen bounds for random sums of centered random variables with finite third moments

Christian Döbler
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Abstract

We show, how the classical Berry-Esseen theorem for normal approximation may be used to derive rates of convergence for random sums of centerd, real-valued random variables with respect to a certain class of probability metrics, including the Kolmogorov and the Wasserstein distances. This technique is applied to several examples, including the approximation by a Laplace distribution of a geometric sum of centered random variables with finite third moment, where a concrete Berry-Esseen bound is derived. This bound reduces to a bound of the supposedly optimal order $\sqrt{p}$ in the i.i.d. case.

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Christian Döbler. 2012-12-21. On rates of convergence and Berry-Esseen bounds for random sums of centered random variables with finite third moments. https://arxiv.org/abs/1212.5401

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