Consistency of the $k$-nearest neighbors rule for functional data

Ahmad Younso

doi:10.5802/crmath.402

Statistiques

Consistency of the

k

-nearest neighbors rule for functional data
[Consistance de la règle des

k

-plus proches voisins pour des données fonctionnelles]

Ahmad Younso ^1,²

¹ MISTEA, Université Montpellier, INRAE, Institut Agro,Montpellier, France
² Department of mathematical statistics, Damascus university, Damascus, Syria

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 237-242.

Résumé
Abstract

Le problème de la classification non paramétrique par la règle des $k$ - plus proches voisins dans un espace métrique général sera considéré. La consistance et la forte consistance du classifieur seront établies sous des conditions légères.

The problem of nonparametric classification by $k$ -nearest neighbors rule in a general metric space will be considered. Consistency and strong consistency of the classifier will be established under mild conditions.

Reçu le : 2021-04-20
Accepté le : 2022-06-26
Publié le : 2023-01-12

DOI : 10.5802/crmath.402

Classification : 00X99

Affiliations des auteurs :

Ahmad Younso ^{1, 2}

¹ MISTEA, Université Montpellier, INRAE, Institut Agro,Montpellier, France
² Department of mathematical statistics, Damascus university, Damascus, Syria

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Ahmad Younso},
     title = {Consistency of the $k$-nearest neighbors rule for functional data},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {237--242},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.402},
     language = {en},
}

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Ahmad Younso. Consistency of the $k$-nearest neighbors rule for functional data. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 237-242. doi : 10.5802/crmath.402. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.402/

Bibliographie
Cité par

[1] Christophe Abraham; Gérard Biau; Benoît Cadre On the kernel rule for function classification, Ann. Inst. Stat. Math., Volume 58 | MR

[2] Gérard Biau; Florentina Bunea; Marten H. Wegkamp Functional classification in Hilbert spaces, IEEE Trans. Inf. Theory, Volume 51 (2005) no. 6, pp. 2163-2172 | DOI | MR | Zbl

[3] Frédéric Cérou; Arnaud Guyader Nearest neighbor classification in infinite dimension, ESAIM, Probab. Stat., Volume 10 (2006), pp. 340-355 | DOI | MR | Zbl

[4] Kamalika Chaudhuri; Sanjoy Dasgupta Rates of Convergence for Nearest Neighbor Classification (2014) | arXiv

[5] Luc Devroye; László Györfi; Adam Krzyżak; Gábor Lugosi On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates, Ann. Stat., Volume 22 (1994) no. 3, pp. 1371-1385 | MR | Zbl

[6] Luc Devroye; László Györfi; Gábor Lugosi A probabilistic Theory of Pattern Recognition, Applications of Mathematics, 31, Springer, 1996 | DOI

[7] Liliana Forzani; Ricardo Fraiman; Pamela Llop Consistent Nonparametric Regression for Functional Data Under the Stone–Besicovitch Conditions, IEEE Trans. Inf. Theory, Volume 58 (2012) no. 11, pp. 6697-6708 | DOI | MR | Zbl

[8] Colin McDiarmid On the method of bounded differences, Surveys of combinatorics (London Mathematical Society Lecture Note Series), Volume 141, Cambridge University Press, 1989, pp. 148-188 | MR | Zbl

[9] Charles J. Stone Consistent nonparametric regression, Ann. Stat., Volume 5 (1977) no. 4, pp. 595-620 | MR | Zbl

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