Statistics
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.

Let (Xi,Yi)i=1,,n be a sequence of strongly mixing random vectors valued in F×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 Yi given Xi. 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.

Soit (Xi,Yi)i=1,,n une suite de vecteurs aléatoires, fortement mélangeants, à valeurs dans F×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 Yi sachant Xi. 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.

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DOI: 10.1016/j.crma.2018.09.001
Almanjahie, Ibrahim M. 1; Chikr Elmezouar, Zouaoui 1; Laksaci, Ali 1; Rachdi, Mustapha 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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     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},
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Almanjahie, Ibrahim M.; Chikr Elmezouar, Zouaoui; Laksaci, Ali; Rachdi, Mustapha. 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. http://www.numdam.org/articles/10.1016/j.crma.2018.09.001/

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