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.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00685928
Contributor : Jérôme Dedecker <>
Submitted on : Friday, April 6, 2012 - 1:22:20 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM

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  • HAL Id : hal-00685928, version 1

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Jérôme Dedecker, Florence Merlevède, Magda Peligrad. Invariance principles for linear processes with application to isotonic regression. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2011, 17, pp.88-113. ⟨hal-00685928⟩

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