Invariance principles for linear processes with application to isotonic regression

Details Invariance principles for linear processes with application to isotonic regression Invariance principles for linear processes with application to isotonic regression

2009-03-11

arxiv.org/abs/0903.1951v2

Bernoulli 2011, Vol. 17, No. 1, 88-113

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ273 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ273

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.

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