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.
Type de document :
Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2011, 17, pp.88-113
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00685928
Contributeur : Jérôme Dedecker <>
Soumis le : vendredi 6 avril 2012 - 13:22:20
Dernière modification le : mardi 11 octobre 2016 - 12:02:49

Identifiants

  • HAL Id : hal-00685928, version 1

Citation

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>

Partager

Métriques

Consultations de la notice

55