In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the limiting distribution is a fractional Brownian motion. The proofs are based on new approximations by a linear process with martingale difference innovations. The results are then applied to study an estimator of the isotonic regression when the error process is a (possibly long-range dependent) time series.
Publié le : 2011-02-15
Classification:
fractional Brownian motion,
generalizations of martingales,
invariance principles,
isotonic regression,
linear processes,
moment inequalities
@article{1297173834,
author = {Dedecker, J\'er\^ome and Merlev\`ede, Florence and Peligrad, Magda},
title = {Invariance principles for linear processes with application to isotonic regression},
journal = {Bernoulli},
volume = {17},
number = {1},
year = {2011},
pages = { 88-113},
language = {en},
url = {http://dml.mathdoc.fr/item/1297173834}
}
Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda. Invariance principles for linear processes with application to isotonic regression. Bernoulli, Tome 17 (2011) no. 1, pp. 88-113. http://gdmltest.u-ga.fr/item/1297173834/