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.
Research supported by the U.S. Office of Naval Research, Contract N 00014-80-C-0613
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van Zwet, W.R. (2012). A Berry-Esseen Bound for Symmetric Statistics. In: van de Geer, S., Wegkamp, M. (eds) Selected Works of Willem van Zwet. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1314-1_13
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