Consider , be a -valued measurable strictly stationary spatial process, where is a semi-metric space. We study a kernel estimator of conditional quantiles of the univariate response variable given the functional variable . The main aim of this Note is to prove the almost complete convergence (with rate) of this estimate.
Étant donné un champ aléatoire fonctionnel, stationnaire (, ) à valeurs dans , où est un espace semi-métrique, de dimension éventuellement infinie. Dans cette Note, on se propose d'étudier la covariation spatiale des deux variables et via l'estimation non paramétrique des quantiles conditionnels de sachant . Nous construisons un estimateur à noyau pour ce modèle non paramétrique spatial et nous établissons sa vitesse de convergence presque complètement.
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@article{CRMATH_2009__347_17-18_1075_0, author = {Laksaci, Ali and Maref, Fouzia}, title = {Estimation non param\'etrique de quantiles conditionnels pour des variables fonctionnelles spatialement d\'ependantes}, journal = {Comptes Rendus. Math\'ematique}, pages = {1075--1080}, publisher = {Elsevier}, volume = {347}, number = {17-18}, year = {2009}, doi = {10.1016/j.crma.2009.06.012}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.012/} }
TY - JOUR AU - Laksaci, Ali AU - Maref, Fouzia TI - Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes JO - Comptes Rendus. Mathématique PY - 2009 SP - 1075 EP - 1080 VL - 347 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.06.012/ DO - 10.1016/j.crma.2009.06.012 LA - fr ID - CRMATH_2009__347_17-18_1075_0 ER -
%0 Journal Article %A Laksaci, Ali %A Maref, Fouzia %T Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes %J Comptes Rendus. Mathématique %D 2009 %P 1075-1080 %V 347 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.06.012/ %R 10.1016/j.crma.2009.06.012 %G fr %F CRMATH_2009__347_17-18_1075_0
Laksaci, Ali; Maref, Fouzia. Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1075-1080. doi : 10.1016/j.crma.2009.06.012. http://www.numdam.org/articles/10.1016/j.crma.2009.06.012/
[1] New Directions in Spatial Econometrics, Springer, Berlin, 1995
[2] Kernel regression estimation for random fields, J. Statist. Plann. Inference, Volume 137 (2007), pp. 778-798
[3] Statistics for Spatial Data, Wiley, New York, 1991
[4] R.M. Crujeiras, W.G. Manteiga, A. Laksaci, E. Ould Saïd, Asymptotic properties for an -norm kernel estimator of the spatial quantile regression for functional data. Technical report, no. 393, Mars 2009, LMPA, Université du Littoral Cote d'Opale, submitted for publication
[5] Kernel regression estimation for continuous spatial processes, Math. Methods Statist., Volume 16 (2007), pp. 298-317
[6] S. Dabo-Niang, A. Laksaci, Spatial conditional quantile regression: Weak consistency of a kernel estimate, 2009, submitted for publication
[7] Asymptotic results of the kernel estimator of the conditional quantile in the normed space under α-mixing hypothesis, Comm. Statist. Theory Methods, Volume 37 (2008), pp. 2735-2759
[8] Nonparametric Functional Data Analysis, Springer Series in Statistics, Springer, New York, 2006
[9] Conditional quantiles for functionally dependent data with application to the climatic El Nino Phenomenon, Sankhyia, Volume 67 (2005), pp. 378-399
[10] Estimating some characteristics of the conditional distribution in nonparametric functional models, Stat. Inference Stoch. Process., Volume 9 (2006), pp. 47-76
[11] Random Fields on a Network – Modeling, Statistics, and Applications, Springer, New York, 1995
[12] M. Hallin, Z. Lu, K. Yu, Local linear spatial quantile regression, Bernoulli (2009), in press
[13] A. Laksaci, E. Ould Saïd, Kernel estimator for the spatial regression quantile : -approach. Technical report, no. 392, Mars 2009, LMPA, Université du Littoral Côte d'Opale, submitted for publication
[14] A generalized -approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality, Statist. Probab. Lett., Volume 79 (2009), pp. 1065-1073
[15] Asymptotic properties of a conditional quantile estimator with randomly truncated data, J. Multivariate Anal., Volume 100 (2009), pp. 546-559
[16] Nonparametric estimation of conditional expectation, J. Statist. Plann. Inference, Volume 139 (2009), pp. 164-175
[17] Spatial Statistics, Wiley, New York, 1981
[18] Non-parametric estimation of conditional quantiles, Statist. Probab. Lett., Volume 7 (1989), pp. 407-412
[19] Consistent nonparametric regression, Discuss. Ann. Statist., Volume 5 (1977), pp. 595-645
[20] Conditional empirical processes, Ann. Statist., Volume 14 (1986), pp. 638-647
[21] Kernel density estimation on random fields, J. Multivariate Anal., Volume 34 (1990), pp. 37-53
[22] E. Youndjé, Estimation non paramétrique de la densité conditionnelle par la méthode du noyau, Thèse de Doctarat, Université de Rouen, 1993
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