Comptes Rendus
Statistics
Consistency of the k-nearest neighbors rule for functional data
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 237-242.

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.

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.

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DOI: 10.5802/crmath.402
Classification: 00X99

Ahmad Younso 1, 2

1 MISTEA, Université Montpellier, INRAE, Institut Agro,Montpellier, France
2 Department of mathematical statistics, Damascus university, Damascus, Syria
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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/

[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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