Note on conditional quantiles for functional ergodic data

Fatima Benziadi; Ali Laksaci; Fethallah Tebboune

doi:10.1016/j.crma.2016.03.005

Statistics

Note on conditional quantiles for functional ergodic data
[Note sur les quantiles conditionnels pour variables fonctionnelles ergodiques]

Présenté par : the Editorial Board

Fatima Benziadi ¹ ; Ali Laksaci ² ; Fethallah Tebboune ³

¹ Université Moulay Taher de Saida, Algeria
² Laboratoire Statistique et Processus stochastiques, Université Djillali-Liabès, BP 89, S. B. A. 22000, Algeria
³ Université Djillali-Liabes, Sidi Bel Abbès, Algeria

Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 628-633.

Abstract (VO)
Résumé

In this Note, we study the recursive kernel estimator of the conditional quantile of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. We establish the almost complete consistency of this estimate when the observations are sampled from a functional ergodic process.

Dans cette Note, nous étudions l'estimateur à noyau récursif des quantiles conditionnels d'une variable réponse réelle Y sachant une variable aléatoire fonctionnelle X. Nous établissons la convergence presque complète de cet estimateur estimation lorsque les observations ont une corrélation ergodique.

Reçu le : 2013-11-14
Accepté le : 2016-03-11
Publié le : 2016-04-11

DOI : 10.1016/j.crma.2016.03.005

Affiliations des auteurs :

Fatima Benziadi ¹ ; Ali Laksaci ² ; Fethallah Tebboune ³

¹ Université Moulay Taher de Saida, Algeria
² Laboratoire Statistique et Processus stochastiques, Université Djillali-Liabès, BP 89, S. B. A. 22000, Algeria
³ Université Djillali-Liabes, Sidi Bel Abbès, Algeria

@article{CRMATH_2016__354_6_628_0,
     author = {Fatima Benziadi and Ali Laksaci and Fethallah Tebboune},
     title = {Note on conditional quantiles for functional ergodic data},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {628--633},
     publisher = {Elsevier},
     volume = {354},
     number = {6},
     year = {2016},
     doi = {10.1016/j.crma.2016.03.005},
     language = {en},
}

TY  - JOUR
AU  - Fatima Benziadi
AU  - Ali Laksaci
AU  - Fethallah Tebboune
TI  - Note on conditional quantiles for functional ergodic data
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 628
EP  - 633
VL  - 354
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2016.03.005
LA  - en
ID  - CRMATH_2016__354_6_628_0
ER  -

%0 Journal Article
%A Fatima Benziadi
%A Ali Laksaci
%A Fethallah Tebboune
%T Note on conditional quantiles for functional ergodic data
%J Comptes Rendus. Mathématique
%D 2016
%P 628-633
%V 354
%N 6
%I Elsevier
%R 10.1016/j.crma.2016.03.005
%G en
%F CRMATH_2016__354_6_628_0

Fatima Benziadi; Ali Laksaci; Fethallah Tebboune. Note on conditional quantiles for functional ergodic data. Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 628-633. doi : 10.1016/j.crma.2016.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.03.005/

Bibliographie
Cité par

[1] A. Amiri; Ch. Crambes; B. Thiam Recursive estimation of nonparametric regression with functional covariate, Comput. Stat. Data Anal., Volume 69 (2014), pp. 154-172

[2] V.I. Bogachev Gaussian Measures, Math. Surv. Monogr., vol. 62, American Mathematical Society, 1999

[3] D. Bosq Linear Processes in Function Spaces: Theory and Applications, Lecture Notes in Statistics, vol. 149, Springer, 2000

[4] S. Dabo-Niang; A. Laksaci Nonparametric quantile regression estimation for functional dependent data, Commun. Stat., Theory Methods, Volume 41 (2011), pp. 1254-1268

[5] S. Dabo-Niang; B. Thiam $L_{1}$ consistency of a kernel estimate of spatial conditional quantile, Stat. Probab. Lett., Volume 80 (2010), pp. 1447-1458

[6] M. Delecroix; A.C. Rosa Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis, J. Nonparametr. Statist., Volume 6 (1996), pp. 367-382

[7] M. Ezzahrioui; E. Ould-Saïd Asymptotic results of a nonparametric conditional quantile estimator for functional time series, Commun. Stat., Theory Methods, Volume 37 (2008), pp. 2735-2759

[8] F. Ferraty; P. Vieu Nonparametric Functional Data Analysis. Theory and Practice, Springer-Verlag, New York, 2006

[9] A. Gheriballah; A. Laksaci; S. Sekkal Nonparametric M-regression for functional ergodic data, Stat. Probab. Lett., Volume 83 (2013), pp. 902-908

[10] N. Laïb; E. Ould-Saïd A robust nonparametric estimation of the autoregression function under an ergodic hypothesis, Can. J. Stat., Volume 28 (2000), pp. 817-828

[11] N. Laïb; D. Louani Nonparametric kernel regression estimate for functional stationary ergodic data: asymptotic properties, J. Multivar. Anal., Volume 101 (2010), pp. 2266-2281

[12] N. Laïb; D. Louani Rates of strong consistencies of the regression function estimator for functional stationary ergodic data, J. Stat. Plan. Inference, Volume 141 (2011), pp. 359-372

[13] A. Laksaci; M. Lemdani; E. Ould-Saïd $L^{1}$ -norm kernel estimator of conditional quantile for functional regressors: consistency and asymptotic normality, Stat. Probab. Lett., Volume 79 (2009), pp. 1065-1073

[14] A. Laksaci; M. Lemdani; E. Ould-Saïd Asymptotic results for an $L^{1}$ -norm kernel estimator of the conditional quantile for functional dependent data with application to climatology, Sankhya, Ser. A, Volume 73 (2011), pp. 125-141

[15] J.O. Ramsay; B.W. Silverman Functional Data Analysis, Springer, New York, 2005

[16] G.R. Roussas; L.T. Tran Asymptotic normality of the recursive kernel regression estimate under dependence conditions, Ann. Stat., Volume 20 (1992), pp. 98-120

[17] M. Samanta Non-parametric estimation of conditional quantiles, Stat. Probab. Lett., Volume 7 (1989), pp. 407-412

[18] C.J. Stone Consistent nonparametric regression. Discussion, Ann. Stat., Volume 5 (1977), pp. 595-645

Cité par Sources :

Commentaires - Politique