Bernoulli

  • Bernoulli
  • Volume 17, Number 1 (2011), 88-113.

Invariance principles for linear processes with application to isotonic regression

Jérôme Dedecker, Florence Merlevède, and Magda Peligrad

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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.

Article information

Source
Bernoulli, Volume 17, Number 1 (2011), 88-113.

Dates
First available in Project Euclid: 8 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1297173834

Digital Object Identifier
doi:10.3150/10-BEJ273

Mathematical Reviews number (MathSciNet)
MR2797983

Zentralblatt MATH identifier
1284.60068

Keywords
fractional Brownian motion generalizations of martingales invariance principles isotonic regression linear processes moment inequalities

Citation

Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda. Invariance principles for linear processes with application to isotonic regression. Bernoulli 17 (2011), no. 1, 88--113. doi:10.3150/10-BEJ273. https://projecteuclid.org/euclid.bj/1297173834


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