[Estimation dans un modèle de régression fonctionnelle spatiale avec dérivées]
Cet article aborde l'estimation de la régression linéaire fonctionnelle dans un cadre spatial. Nous étudions les propriétés asymptotiques de l'estimateur d'un modèle où une variable réponse réelle est liée à une variable dépendante fonctionnelle et sa dérivée. Nous établissons des résultats de convergence pour cet estimateur, et des vitesses de convergence sont données.
This paper deals with functional linear regression for spatial data. We study the asymptotic properties of an estimator of a linear model where a spatial scalar response variable is related to a spatial functional explanatory variable and to its derivative. Convergence results with rate of this estimator are derived.
Accepté le :
Publié le :
@article{CRMATH_2018__356_5_558_0,
author = {Bouka, St\'ephane and Dabo-Niang, Sophie and Nkiet, Guy Martial},
title = {On estimation in a spatial functional linear regression model with derivatives},
journal = {Comptes Rendus. Math\'ematique},
pages = {558--562},
publisher = {Elsevier},
volume = {356},
number = {5},
year = {2018},
doi = {10.1016/j.crma.2018.02.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.02.013/}
}
TY - JOUR AU - Bouka, Stéphane AU - Dabo-Niang, Sophie AU - Nkiet, Guy Martial TI - On estimation in a spatial functional linear regression model with derivatives JO - Comptes Rendus. Mathématique PY - 2018 SP - 558 EP - 562 VL - 356 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.02.013/ DO - 10.1016/j.crma.2018.02.013 LA - en ID - CRMATH_2018__356_5_558_0 ER -
%0 Journal Article %A Bouka, Stéphane %A Dabo-Niang, Sophie %A Nkiet, Guy Martial %T On estimation in a spatial functional linear regression model with derivatives %J Comptes Rendus. Mathématique %D 2018 %P 558-562 %V 356 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.02.013/ %R 10.1016/j.crma.2018.02.013 %G en %F CRMATH_2018__356_5_558_0
Bouka, Stéphane; Dabo-Niang, Sophie; Nkiet, Guy Martial. On estimation in a spatial functional linear regression model with derivatives. Comptes Rendus. Mathématique, Tome 356 (2018) no. 5, pp. 558-562. doi : 10.1016/j.crma.2018.02.013. http://www.numdam.org/articles/10.1016/j.crma.2018.02.013/
[1] Adaptive functional linear regression, Ann. Stat., Volume 40 (2012), pp. 2765-2797
[2] A partial overview of the theory of statistics with functional data, J. Stat. Plan. Inference, Volume 147 (2014), pp. 1-23
[3] Cokriging based on curves, prediction and estimation of the prediction variance, InterStat, Volume 2 (2014), pp. 1-30
[4] Ordinary kriging for function-valued spatial data, Environ. Ecol. Stat., Volume 18 (2011) no. 3, pp. 411-426
[5] Random Fields on a Network: Modeling, Statistics and Applications, Springer, New York, 1995
[6] A statistical view of some chemometrics regression tools: discussion, Technometrics, Volume 35 (1993), pp. 140-143
[7] Inference for Functional Data with Applications, Springer, 2012
[8] Estimating functional linear mixed-effects regression models, Comput. Stat. Data Anal., Volume 106 (2017), pp. 153-164
[9] Functional linear regression with derivatives, J. Nonparametr. Stat., Volume 21 (2009), pp. 19-40
[10] Cokriging for spatial functional data, J. Multivar. Anal., Volume 101 (2010) no. 2, pp. 409-418
[11] Kernel density estimation on random fields, J. Multivar. Anal., Volume 34 (1990), pp. 37-53
Cité par Sources :
