Optimal rates of convergence in the CLT for quadratic forms
Bentkus, V. ; Götze, F.
Ann. Probab., Tome 24 (1996) no. 2, p. 466-490 / Harvested from Project Euclid
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We prove optimal convergence rates in the central limit theorem for sums ${\bf R}^k.$ Assuming a fourth moment, we obtain a Berry-Esseen type bound of $O(N^{-1})$ for the probability of hitting a ball provided that $k\leq 5$. The proof still requires a technical assumption related to the independence of coordinate sums.
Publié le : 1996-01-14
Classification:  
@article{1042644727,
     author = {Bentkus, V. and G\"otze, F.},
     title = {Optimal rates of convergence in the CLT for quadratic
			 forms},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 466-490},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644727}
}

Bentkus, V.; Götze, F. Optimal rates of convergence in the CLT for quadratic
			 forms. Ann. Probab., Tome 24 (1996) no. 2, pp.  466-490. http://gdmltest.u-ga.fr/item/1042644727/