On the Berry-Esseen Theorem for $U$-Statistics

Chan, Y.-K.; Wierman, John

Ann. Probab., Tome 5 (1977) no. 6, p. 136-139 / Harvested from Project Euclid

Résumé

Assuming the existence of fourth moment only, we prove the Berry-Esseen theorem for $U$-statistics. Assuming the third absolute moment, we obtain the order bound $O(n^{-\frac{1}{2}} \log^{\frac{1}{3}}n)$. This improves earlier results of Bickel, and Grams and Serfling.

Publié le : 1977-02-14
Classification: Berry-Esseen bounds, $U$-statistics, 60F07

@article{1176995897,
     author = {Chan, Y.-K. and Wierman, John},
     title = {On the Berry-Esseen Theorem for $U$-Statistics},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 136-139},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995897}
}

Chan, Y.-K.; Wierman, John. On the Berry-Esseen Theorem for $U$-Statistics. Ann. Probab., Tome 5 (1977) no. 6, pp.  136-139. http://gdmltest.u-ga.fr/item/1176995897/