Lower bounds for tails of sums of independent symmetric random variables

Lutz Mattner

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Lower bounds for tails of sums of independent symmetric random variables

Lutz Mattner

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Abstract

The approach of Kleitman (1970) and Kanter (1976) to multivariate concentration function inequalities is generalized in order to obtain for deviation probabilities of sums of independent symmetric random variables a lower bound depending only on deviation probabilities of the terms of the sum. This bound is optimal up to discretization effects, improves on a result of Nagaev (2001), and complements the comparison theorems of Birnbaum (1948) and Pruss (1997). Birnbaum's theorem for unimodal random variables is extended to the lattice case.

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Lutz Mattner. 2006-09-07. Lower bounds for tails of sums of independent symmetric random variables. https://arxiv.org/abs/math/0609200

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