Invariance principles for linear processes with application to isotonic regression
Abstract
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.
Cite
@article{arxiv.0903.1951,
title = {Invariance principles for linear processes with application to isotonic regression},
author = {Jérôme Dedecker and Florence Merlevède and Magda Peligrad},
journal= {arXiv preprint arXiv:0903.1951},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.3150/10-BEJ273 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)