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A Berry-Esseen Bound for Symmetric Statistics

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

Summary

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.

Keywords

Symmetric Function Independent Random Variable Symmetric Statistics Finite Variance Edgeworth Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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