Statistics
Nonparametric estimation of the density of the regression noise
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 461-466.

This Note presents an estimator of the density of the error in a homoscedastic regression model, based on model selection methods, and propose a bound for the quadratic integrated risk.

Cette Note présente un estimateur de la loi de l'erreur dans un modèle de régression homoscédastique, basé sur des techniques de sélection de modèle, et propose une majoration du risque quadratique intégré.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.021
Plancade, Sandra 1

1 MAP5, UMR 8145, Université Paris Descartes, 45, rue des Saints-Pères, 75270 Paris cedex 06, France
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Plancade, Sandra. Nonparametric estimation of the density of the regression noise. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 461-466. doi : 10.1016/j.crma.2008.02.021. http://www.numdam.org/articles/10.1016/j.crma.2008.02.021/

[1] Baraud, Y. Model selection for regression on a random design, ESAIM Probab. Statist., Volume 6 (2002), pp. 127-146

[2] Baraud, Y. Model selection for regression on a fixed design, Probab. Theory Related Fields, Volume 117 (2000), pp. 467-493

[3] DeVore, R.A.; Lorentz, G.G. Constructive Approximation, Springer-Verlag, 1993

[4] Efromovich, S. Estimation of the density of regression errors, Annals of Statistics, Volume 33 (2005), pp. 2194-2227

[5] Härdle, W.; Kerbyacharian, G.; Picard, D.; Tsybakov, A. Wavelets, Approximation, and Statistical Applications, Lecture Notes in Statistics, vol. 129, 1998

[6] C. Lacour, Adaptative estimation of the transition density of a particular hidden Markov chain, J. Multivariate Anal. 2006, in press, available online; arXiv: math/0611681v1 [math.ST], hal-00115612, version 1

[7] Massart, P. Concentration inequalities and model selection, July 6–23, 2003 (Lecture Notes in Mathematics), Volume vol. 1896 (2007)

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