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Lower bounds for tails of sums of independent symmetric random variables

Probability 2007-05-23 v1

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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Cite

@article{arxiv.math/0609200,
  title  = {Lower bounds for tails of sums of independent symmetric random variables},
  author = {Lutz Mattner},
  journal= {arXiv preprint arXiv:math/0609200},
  year   = {2007}
}

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7 pages