Functional time series prediction via conditional mode estimation

Frédéric Ferraty; Ali Laksaci; Philippe Vieu

doi:10.1016/j.crma.2005.01.016

Statistics/Probability Theory

Functional time series prediction via conditional mode estimation

Presented by: Paul Deheuvels

Frédéric Ferraty ¹; Ali Laksaci ²; Philippe Vieu ¹

¹ Laboratoire de statistique et probabilités, Université Paul Sabatier, 31062 Toulouse, France
² Université Djillali Liabes, Sidi Bel Abbes, Algeria

Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 389-392.

Abstract
Résumé

This Note focuses on an estimator of the conditional mode of a scalar response Y given a functional random variable X. We start by building a kernel estimator of the conditional density of Y given X; the conditional mode is defined as the value which maximizes this conditional density. We establish the almost complete convergence for this estimate under α-mixing assumption.

On établit la convergence presque-complète de l'estimateur du mode de la distribution d'une variable réelle Y conditionnée par une variable fonctionnelle X. Le mode conditionnel est estimé par la valeur qui maximise l'estimateur à noyau de la densité conditionnelle de Y sachant X. Des résultats asymptotiques concernant cet estimateur sont établis sous l'hypothèse α-mélangeante, rendant nos résultats opérationnels en prédiction de séries chronologiques.

Received: 2004-07-09
Accepted: 2005-01-18
Published online: 2005-02-12

DOI: 10.1016/j.crma.2005.01.016

Author's affiliations:

Frédéric Ferraty ¹; Ali Laksaci ²; Philippe Vieu ¹

¹ Laboratoire de statistique et probabilités, Université Paul Sabatier, 31062 Toulouse, France
² Université Djillali Liabes, Sidi Bel Abbes, Algeria

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     author = {Fr\'ed\'eric Ferraty and Ali Laksaci and Philippe Vieu},
     title = {Functional time series prediction via conditional mode estimation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {389--392},
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     number = {5},
     year = {2005},
     doi = {10.1016/j.crma.2005.01.016},
     language = {en},
}

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Frédéric Ferraty; Ali Laksaci; Philippe Vieu. Functional time series prediction via conditional mode estimation. Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 389-392. doi : 10.1016/j.crma.2005.01.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.016/

References
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