BERRY-ESSEEN BOUNDS FOR STATISTICS OF WEAKLY DEPENDENT SAMPLES

Authors
BENTKUS V GOTZE F TIKHOMIROV A
Citation
V. Bentkus et al., BERRY-ESSEEN BOUNDS FOR STATISTICS OF WEAKLY DEPENDENT SAMPLES, Bernoulli, 3(3), 1997, pp. 329-349
Citations number
24
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Bernoulli → ACNP
ISSN journal
13507265
Volume
3
Issue
3
Year of publication
1997
Pages
329 - 349
Database
ISI
SICI code
1350-7265(1997)3:3<329:BBFSOW>2.0.ZU;2-C
Abstract
We prove Berry-Esseen bounds for a general class of asymptotically nor mal statistics which are functions of N weakly dependent random variab les under easily verifiable conditions. In particular, we show, for so me delta > 0, the validity of the bound O(N-1/2 log(delta) N) for U-st atistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order sta tistics.