OPTIMAL RATES OF CONVERGENCE IN THE CLT FOR QUADRATIC-FORMS

Authors
BENTKUS V GOTZE F
Citation
V. Bentkus et F. Gotze, OPTIMAL RATES OF CONVERGENCE IN THE CLT FOR QUADRATIC-FORMS, Annals of probability, 24(1), 1996, pp. 466-490
Citations number
39
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
24
Issue
1
Year of publication
1996
Pages
466 - 490
Database
ISI
SICI code
0091-1798(1996)24:1<466:OROCIT>2.0.ZU;2-E
Abstract
We prove optimal convergence rates in the central limit theorem for su ms in R(k). Assuming a fourth moment, we obtain a Berry-Esseen type bo und of O(N-1) for the probability of hitting a ball provided that k gr eater than or equal to 5. The proof still requires a technical assumpt ion related to the independence of coordinates of sums.