We address the problem of consistency of the $k$-nearest neighbors kernel estimators of the density and the regression function in the multivariate case. We get the rates of strong uniform consistency on the whole space $\mathbb{R}^p$ for these estimators under specified assumptions.
Cet article aborde le problème de la convergence des estimateurs de la densité et de la fonction de régression par la méthode des $k$ plus proches voisins, dans le cas multivarié. Nous déterminons les vitesses de convergence uniforme presque sûre sur tout l’espace $\mathbb{R}^p$, sous des conditions spécifiées.
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Keywords: $k$-nearest neighbors, kernel estimators, density, regression function, strong uniform consistency, rates of convergence
Mots-clés : $k$ plus proches voisins, estimateurs à noyau, densité, fonction de régression, convergence uniforme presque sûre, vitesse de convergence
Luran Bengono Mintogo 1; Emmanuel de Dieu Nkou 1; Guy Martial Nkiet 1
CC-BY 4.0
@article{CRMATH_2025__363_G10_1035_0,
author = {Luran Bengono Mintogo and Emmanuel de Dieu Nkou and Guy Martial Nkiet},
title = {Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function},
journal = {Comptes Rendus. Math\'ematique},
pages = {1035--1046},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
doi = {10.5802/crmath.784},
language = {en},
}
TY - JOUR AU - Luran Bengono Mintogo AU - Emmanuel de Dieu Nkou AU - Guy Martial Nkiet TI - Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function JO - Comptes Rendus. Mathématique PY - 2025 SP - 1035 EP - 1046 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.784 LA - en ID - CRMATH_2025__363_G10_1035_0 ER -
%0 Journal Article %A Luran Bengono Mintogo %A Emmanuel de Dieu Nkou %A Guy Martial Nkiet %T Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function %J Comptes Rendus. Mathématique %D 2025 %P 1035-1046 %V 363 %I Académie des sciences, Paris %R 10.5802/crmath.784 %G en %F CRMATH_2025__363_G10_1035_0
Luran Bengono Mintogo; Emmanuel de Dieu Nkou; Guy Martial Nkiet. Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1035-1046. doi: 10.5802/crmath.784
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