The Berry-Esseen Theorem for $U$-Statistics
Callaert, Herman ; Janssen, Paul
Ann. Statist., Tome 6 (1978) no. 1, p. 417-421 / Harvested from Project Euclid
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Assuming only the existence of the third absolute moment we prove that $\sup_x |P(\sigma_n^{-1} U_n \leqq x) - \Phi (x)| \leqq C_{\nu_3\sigma_g}^{-3}n^{-\frac{1}{2}}$ where $U_n$ is a $U$-statistic. This concludes a series of investigations on the Berry-Esseen theorem for $U$-statistics by Grams and Serfling, Bickel, and Chan and Wierman.
Publié le : 1978-03-14
Classification:  Berry-Esseen bound,  $U$-statistics,  60F05 
@article{1176344132,
     author = {Callaert, Herman and Janssen, Paul},
     title = {The Berry-Esseen Theorem for $U$-Statistics},
     journal = {Ann. Statist.},
     volume = {6},
     number = {1},
     year = {1978},
     pages = { 417-421},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176344132}
}

Callaert, Herman; Janssen, Paul. The Berry-Esseen Theorem for $U$-Statistics. Ann. Statist., Tome 6 (1978) no. 1, pp.  417-421. http://gdmltest.u-ga.fr/item/1176344132/