On the estimation of density-weighted average derivative by wavelet methods under various dependence structures

Abstract : The problem of estimating the density-weighted average derivative of a regression function is considered. We present a new consistent estimator based on a plug-in approach and wavelet projections. Its performances are explored under various dependence structures on the observations: the independent case, the $\rho$-mixing case and the $\alpha$-mixing case. More precisely, denoting $n$ the number of observations, in the independent case, we prove that it attains $1/n$ under the mean squared error, in the $\rho$-mixing case, $1/\sqrt{n}$ under the mean absolute error, and, in the $\alpha$-mixing case, $\sqrt{\ln n /n}$ under the mean absolute error. A short simulation study illustrates the theory.
Type de document :
Article dans une revue
Sankhya A, Springer Verlag, 2014, 〈10.1007/s13171-013-0032-1〉
Liste complète des métadonnées

Littérature citée [42 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00668544
Contributeur : Christophe Chesneau <>
Soumis le : vendredi 31 mai 2013 - 11:40:22
Dernière modification le : jeudi 21 juin 2018 - 17:14:02
Document(s) archivé(s) le : dimanche 1 septembre 2013 - 04:10:57

Fichier

average3-dens-wav.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Christophe Chesneau, Maher Kachour, Fabien Navarro. On the estimation of density-weighted average derivative by wavelet methods under various dependence structures. Sankhya A, Springer Verlag, 2014, 〈10.1007/s13171-013-0032-1〉. 〈hal-00668544v3〉

Partager

Métriques

Consultations de la notice

444

Téléchargements de fichiers

384