We establish strong and weak approximations for quadratic forms of
weakly and strongly dependent random variables and obtain necessary and
sufficient conditions for the weak convergence of weighted functions of
quadratic forms. The results are applied to get the asymptotic distributions of
some tests which can be used to detect possible changes in the long-memory
parameter.
Publié le : 1999-02-14
Classification:
Strong and weak approximations,
change-point,
quadratic forms,
limit theorems,
weight functions,
linear process,
long-memory parameter,
60F17,
60F03,
60F15,
60G70
@article{1029962600,
author = {Horv\'ath, Lajos and Shao, Qi-Man},
title = {Limit theorems for quadratic forms with applications to Whittle's
estimate},
journal = {Ann. Appl. Probab.},
volume = {9},
number = {1},
year = {1999},
pages = { 146-187},
language = {en},
url = {http://dml.mathdoc.fr/item/1029962600}
}
Horváth, Lajos; Shao, Qi-Man. Limit theorems for quadratic forms with applications to Whittle's
estimate. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp. 146-187. http://gdmltest.u-ga.fr/item/1029962600/