<i>k</i>NN local linear estimation of the conditional cumulative distribution function: Dependent functional data case

Ibrahim M. Almanjahie; Zouaoui Chikr Elmezouar; Ali Laksaci; Mustapha Rachdi

doi:10.1016/j.crma.2018.09.001

Statistics

kNN local linear estimation of the conditional cumulative distribution function: Dependent functional data case
[Analyse des séries temporelles fonctionnelles : estimation locale linéaire et par les k plus proches voisins de la fonction de répartition conditionnelle]

Présenté par : Paul Deheuvels

Ibrahim M. Almanjahie ¹ ; Zouaoui Chikr Elmezouar ¹ ; Ali Laksaci ¹ ; Mustapha Rachdi ²

¹ Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
² Université Grenoble Alpes, Laboratoire AGEIS, EA 7407, AGIM–TIMB Team, UFR SHS, BP 47, 38040 Grenoble cedex 09, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 10, pp. 1036-1039.

Résumé
Abstract

Soit ${(X_{i}, Y_{i})}_{i = 1, \dots, n}$ une suite de vecteurs aléatoires, fortement mélangeants, à valeurs dans $F \times R$ , où $F$ est un espace de Hilbert. Dans cette note, nous nous intéressons au problème d'estimation locale linéaire de la distribution conditionnelle de $Y_{i}$ sachant $X_{i}$ . Les objectifs principaux de cette note sont donc (i) de construire un estimateur local linéaire rapide, en introduisant la technique des k plus proches voisins, de la distribution conditionnelle et (ii) de prouver sa consistance forte dans le cadre des séries temporelles conditionnelles.

Let ${(X_{i}, Y_{i})}_{i = 1, \dots, n}$ be a sequence of strongly mixing random vectors valued in $F \times R$ , where $F$ is a Hilbert space. This note deals with the problem of the local linear estimation of the conditional cumulative distribution function of $Y_{i}$ given $X_{i}$ . Then, the main goals of this note are (i) to construct a fast kNN local linear estimate of the conditional distribution function, and (ii) to prove its strong consistency in the functional time series analysis situation.

Reçu le : 2018-06-11
Accepté le : 2018-09-10
Publié le : 2018-09-27

DOI : 10.1016/j.crma.2018.09.001

Affiliations des auteurs :

Ibrahim M. Almanjahie ¹ ; Zouaoui Chikr Elmezouar ¹ ; Ali Laksaci ¹ ; Mustapha Rachdi ²

¹ Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
² Université Grenoble Alpes, Laboratoire AGEIS, EA 7407, AGIM–TIMB Team, UFR SHS, BP 47, 38040 Grenoble cedex 09, France

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     author = {Ibrahim M. Almanjahie and Zouaoui Chikr Elmezouar and Ali Laksaci and Mustapha Rachdi},
     title = {\protect\emph{k}NN local linear estimation of the conditional cumulative distribution function: {Dependent} functional data case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1036--1039},
     publisher = {Elsevier},
     volume = {356},
     number = {10},
     year = {2018},
     doi = {10.1016/j.crma.2018.09.001},
     language = {en},
}

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Ibrahim M. Almanjahie; Zouaoui Chikr Elmezouar; Ali Laksaci; Mustapha Rachdi. kNN local linear estimation of the conditional cumulative distribution function: Dependent functional data case. Comptes Rendus. Mathématique, Volume 356 (2018) no. 10, pp. 1036-1039. doi : 10.1016/j.crma.2018.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.09.001/

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