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A shorter proof of Kanter’s Bessel function concentration bound
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  • Published: 12 December 2006

A shorter proof of Kanter’s Bessel function concentration bound

  • Lutz Mattner1 &
  • Bero Roos2 

Probability Theory and Related Fields volume 139, pages 191–205 (2007)Cite this article

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  • 28 Citations

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Abstract

We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I0(x) + I1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Čekanavičius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität zu Lübeck, Wallstr. 40, 23560, Lübeck, Germany

    Lutz Mattner

  2. Department Mathematik, SPST, Universität Hamburg, Bundesstr. 55, 20146, Hamburg, Germany

    Bero Roos

Authors
  1. Lutz Mattner
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  2. Bero Roos
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Corresponding author

Correspondence to Lutz Mattner.

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Mattner, L., Roos, B. A shorter proof of Kanter’s Bessel function concentration bound. Probab. Theory Relat. Fields 139, 191–205 (2007). https://doi.org/10.1007/s00440-006-0043-0

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  • Received: 21 March 2006

  • Revised: 23 October 2006

  • Published: 12 December 2006

  • Issue Date: September 2007

  • DOI: https://doi.org/10.1007/s00440-006-0043-0

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Keywords

  • Analytic inequalities
  • Bernoulli convolution
  • Modified Bessel function
  • Concentration function
  • Poisson binomial distribution
  • Symmetric three point convolution
  • Symmetrized Poisson distribution

Mathematics Subject Classification (2000)

  • 60E15
  • 60G50
  • 33C10
  • 26D07
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