A Berry-Esseen Bound for Symmetric Statistics

  • W. R. van Zwet
Open Access
Part of the Selected Works in Probability and Statistics book series (SWPS)


The rate of convergence of the distribution function of a symmetric function of N independent and identically distributed random variables to its normal limit is investigated. Under appropriate moment conditions the rate is shown to be (\(O\left( {{N^{ - \frac{1}{2}}}} \right)\)). This theorem generalizes many known results for special cases and two examples are given. Possible further extensions are indicated.


Symmetric Function Independent Random Variable Symmetric Statistics Finite Variance Edgeworth Expansion 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • W. R. van Zwet
    • 1
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of LeidenLeidenThe Netherlands

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