We consider quadratic forms
Q_n = \sum_{1 \le j \neq k \le n} a_{jk}X_j X_k,
where $X_j$ are i.i.d. random variables with finite
third moment. We obtain optimal bounds for the Kolmogorov distance between the
distribution of $Q_n$ and the distribution of the same quadratic forms with
$X_j$ replaced by corresponding Gaussian random variables. These bounds are
applied to Toeplitz and random matrices as well as to nonstationary AR(1)
processes.
Publié le : 1999-04-15
Classification:
Independent random variables,
quadratic forms,
asymptotic distribution,
limit theorems,
Berry–Esseen bounds,
60F05
@article{1022677395,
author = {G\"otze, F. and Tikhomirov, A. N.},
title = {Asymptotic Distribution of Quadratic Forms},
journal = {Ann. Probab.},
volume = {27},
number = {1},
year = {1999},
pages = { 1072-1098},
language = {en},
url = {http://dml.mathdoc.fr/item/1022677395}
}
Götze, F.; Tikhomirov, A. N. Asymptotic Distribution of Quadratic Forms. Ann. Probab., Tome 27 (1999) no. 1, pp. 1072-1098. http://gdmltest.u-ga.fr/item/1022677395/