Nonparametric estimation of the density of regression errors

Rawane Samb

doi:10.1016/j.crma.2011.10.017

Probability Theory/Statistics

Nonparametric estimation of the density of regression errors
[Estimation nonparamétrique de la densité des erreurs de régression]

Présenté par : Paul Deheuvels

Rawane Samb ¹

¹ ISBA, Université Catholique de Louvain, 20, voie du Roman pays, B-1348 Louvain-la-Neuve, Belgium

Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1281-1285.

Abstract (VO)
Résumé

Consider the nonparametric regression model $Y = m (X) + ε$ , where the function m is smooth but unknown, and ε is independent of X. An estimator of the density of the error term ε is proposed and its weak consistency is obtained. The strategy used here is based on the kernel estimation of the residuals. Our contribution is twofold. First, we evaluate the impact of the estimation of the regression function m on the error density estimator. Secondly, the optimal choices of the first and second-step bandwidths used for estimating the regression function and the error density respectively, are proposed. Further, we investigate the asymptotic normality of the error density estimator and its rate-optimality.

Nous présentons un estimateur nonparamétrique de la densité de lʼerreur dans le modèle de régression $Y = m (X) + ε$ , où la fonction m est lisse mais inconnue, et le terme dʼerreur ε est indépendant de X. Lʼestimateur proposé est basé sur une estimation nonparamétrique des résidus, et sa consistance faible est obtenue. Notre contribution se situe à deux niveaux. Dʼabord, nous évaluons lʼimpact de lʼestimation de la fonction de régression sur lʼestimateur final de la densité de lʼerreur. Ensuite, nous proposons les choix optimaux des fenêtres de première et de deuxième étape utilisées respectivement pour les estimations de m et de la densité des résidus. Nous étudions également la normalié asymptotique de lʼestimateur de la densité de lʼerreur et sa vitesse de convergence.

Reçu le : 2011-08-19
Accepté le : 2011-10-19
Publié le : 2011-11-09

DOI : 10.1016/j.crma.2011.10.017

Affiliations des auteurs :

Rawane Samb ¹

¹ ISBA, Université Catholique de Louvain, 20, voie du Roman pays, B-1348 Louvain-la-Neuve, Belgium

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     title = {Nonparametric estimation of the density of regression errors},
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     year = {2011},
     doi = {10.1016/j.crma.2011.10.017},
     language = {en},
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Rawane Samb. Nonparametric estimation of the density of regression errors. Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1281-1285. doi : 10.1016/j.crma.2011.10.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.017/

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