A shorter proof of Kanter's Bessel function concentration bound

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Erscheinungsjahr:
2007
Medientyp:
Text
Schlagworte:
  • Analytic inequalities
  • Bernoulli convolution
  • Concentration function
  • Modified Bessel function
  • Poisson binomial distribution
  • Symmetric three point convolution
  • Symmetrized Poisson distribution
Beschreibung:
  • 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). © Springer-Verlag 2007.
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  • info:eu-repo/semantics/closedAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/65250b55-5e75-4391-b8ea-82ae087e6d3d