Open Access 2012 | OriginalPaper | Buchkapitel
A Berry-Esseen Bound for Symmetric Statistics
verfasst von : W. R. van Zwet
Erschienen in: Selected Works of Willem van Zwet
Verlag: Springer New York
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.