Large deviations theorems in nonparametric regression on functional data

Mohamed Cherfi

doi:10.1016/j.crma.2011.04.011

Statistics

Large deviations theorems in nonparametric regression on functional data

Presented by: Paul Deheuvels

Mohamed Cherfi ¹

¹ Laboratoire de statistique théorique et appliquée (LSTA), équipe dʼAccueil 3124, université Pierre et Marie Curie – Paris 6, tour 15-25, 2ème étage, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 583-585.

Abstract
Résumé

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.

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.

Received: 2010-05-19
Accepted: 2011-04-19
Published online: 2011-05-01

DOI: 10.1016/j.crma.2011.04.011

Author's affiliations:

Mohamed Cherfi ¹

¹ Laboratoire de statistique théorique et appliquée (LSTA), équipe dʼAccueil 3124, université Pierre et Marie Curie – Paris 6, tour 15-25, 2ème étage, 4, place Jussieu, 75252 Paris cedex 05, France

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     title = {Large deviations theorems in nonparametric regression on functional data},
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     doi = {10.1016/j.crma.2011.04.011},
     language = {en},
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Mohamed Cherfi. Large deviations theorems in nonparametric regression on functional data. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 583-585. doi : 10.1016/j.crma.2011.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.011/

References
Cited by

[1] R.R. Bahadur 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] N. Berrahou; D. Louani Efficiency of some tests when testing symmetry hypothesis, J. Nonparametr. Stat., Volume 18 (2006) no. 7–8, pp. 465-482 (2007)

[3] A. Dembo; O. Zeitouni Large Deviations Techniques and Applications, Appl. Math. (New York), vol. 38, Springer-Verlag, New York, 1998

[4] F. Ferraty; P. Vieu 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] F. Ferraty; P. Vieu Nonparametric functional data analysis, Theory and Practice, Springer Ser. Statist., Springer, New York, 2006

[6] F. Ferraty; P. Vieu 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] F. Ferraty; A. Mas; P. Vieu Nonparametric regression on functional data: inference and practical aspects, Aust. N. Z. J. Stat., Volume 49 (2007) no. 3, pp. 267-286

[8] F. Ferraty; A. Laksaci; A. Tadj; P. Vieu Rate of uniform consistency for nonparametric estimates with functional variables, J. Statist. Plann. Inference, Volume 140 (2010) no. 2, pp. 335-352

[9] C. Joutard Sharp large deviations in nonparametric estimation, J. Nonparametr. Stat., Volume 18 (2006) no. 3, pp. 293-306

[10] A. Korostelev A minimaxity criterion in nonparametric regression based on large-deviations probabilities, Ann. Statist., Volume 24 (1996) no. 3, pp. 1075-1083

[11] D. Louani Large deviations limit theorems for the kernel density estimator, Scand. J. Statist., Volume 25 (1998) no. 1, pp. 243-253

[12] D. Louani Some large deviations limit theorems in conditional nonparametric statistics, Statistics, Volume 33 (1999) no. 2, pp. 171-196

[13] A. Mokkadem; M. Pelletier; B. Thiam Large and moderate deviations principles for kernel estimators of the multivariate regression, Math. Methods Statist., Volume 17 (2008) no. 2, pp. 146-172

[14] Y. Nikitin Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press, Cambridge, 1995

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