[Théorèmes de grandes déviations pour la régression non paramétrique sur des données fonctionnelles]
Lʼobjet de cette Note est dʼétablir un principe de grandes déviations ponctuel et un principe de grandes déviations uniforme pour lʼestimateur à noyau de la régression sur des données fonctionnelles.
In this Note we prove large deviations principles for the Nadaraya–Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems.
Accepté le :
Publié le :
@article{CRMATH_2011__349_9-10_583_0,
author = {Cherfi, Mohamed},
title = {Large deviations theorems in nonparametric regression on functional data},
journal = {Comptes Rendus. Math\'ematique},
pages = {583--585},
publisher = {Elsevier},
volume = {349},
number = {9-10},
year = {2011},
doi = {10.1016/j.crma.2011.04.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.04.011/}
}
TY - JOUR AU - Cherfi, Mohamed TI - Large deviations theorems in nonparametric regression on functional data JO - Comptes Rendus. Mathématique PY - 2011 SP - 583 EP - 585 VL - 349 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.04.011/ DO - 10.1016/j.crma.2011.04.011 LA - en ID - CRMATH_2011__349_9-10_583_0 ER -
%0 Journal Article %A Cherfi, Mohamed %T Large deviations theorems in nonparametric regression on functional data %J Comptes Rendus. Mathématique %D 2011 %P 583-585 %V 349 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.04.011/ %R 10.1016/j.crma.2011.04.011 %G en %F CRMATH_2011__349_9-10_583_0
Cherfi, Mohamed. Large deviations theorems in nonparametric regression on functional data. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 583-585. doi : 10.1016/j.crma.2011.04.011. http://www.numdam.org/articles/10.1016/j.crma.2011.04.011/
[1] Some limit theorems in statistics, Conference Board of the Mathematical Sciences Regional Conference Series, Appl. Math., vol. 4, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1971
[2] Efficiency of some tests when testing symmetry hypothesis, J. Nonparametr. Stat., Volume 18 (2006) no. 7–8, pp. 465-482 (2007)
[3] Large Deviations Techniques and Applications, Appl. Math. (New York), vol. 38, Springer-Verlag, New York, 1998
[4] Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination, J. Nonparametr. Stat., Volume 16 (2004) no. 1–2, pp. 111-125
[5] Nonparametric functional data analysis, Theory and Practice, Springer Ser. Statist., Springer, New York, 2006
[6] Erratum of: “Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination” [J. Nonparametr. Stat. 16 (1–2) (2004) 111–125], J. Nonparametr. Stat., Volume 20 (2008) no. 2, pp. 187-189
[7] Nonparametric regression on functional data: inference and practical aspects, Aust. N. Z. J. Stat., Volume 49 (2007) no. 3, pp. 267-286
[8] Rate of uniform consistency for nonparametric estimates with functional variables, J. Statist. Plann. Inference, Volume 140 (2010) no. 2, pp. 335-352
[9] Sharp large deviations in nonparametric estimation, J. Nonparametr. Stat., Volume 18 (2006) no. 3, pp. 293-306
[10] A minimaxity criterion in nonparametric regression based on large-deviations probabilities, Ann. Statist., Volume 24 (1996) no. 3, pp. 1075-1083
[11] Large deviations limit theorems for the kernel density estimator, Scand. J. Statist., Volume 25 (1998) no. 1, pp. 243-253
[12] Some large deviations limit theorems in conditional nonparametric statistics, Statistics, Volume 33 (1999) no. 2, pp. 171-196
[13] Large and moderate deviations principles for kernel estimators of the multivariate regression, Math. Methods Statist., Volume 17 (2008) no. 2, pp. 146-172
[14] Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press, Cambridge, 1995
Cité par Sources :
