Normal approximation for nonlinear statistics using a concentration inequality approach

Chen, Louis H.Y.; Shao, Qi-Man

Bernoulli, Tome 13 (2007) no. 1, p. 581-599 / Harvested from Project Euclid

Résumé

Let T be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry–Esseen type bounds for T are obtained. The bounds are the best possible for many known statistics. Applications to U-statistics, multisample U-statistics, L-statistics, random sums and functions of nonlinear statistics are discussed.

Publié le : 2007-05-14
Classification: concentration inequality approach, L-statistics, multisample U-statistics, non-uniform Berry–Esseen bound, nonlinear statistics, normal approximation, U-statistics, uniform Berry–Esseen bound

@article{1179498762,
     author = {Chen, Louis H.Y. and Shao, Qi-Man},
     title = {Normal approximation for nonlinear statistics using a concentration inequality approach},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 581-599},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1179498762}
}

Chen, Louis H.Y.; Shao, Qi-Man. Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli, Tome 13 (2007) no. 1, pp.  581-599. http://gdmltest.u-ga.fr/item/1179498762/