Le problème dʼintérêt est dʼestimer la fonction de concentration et lʼaire sous la courbe (AUC) à travers lʼestimation des paramètres dʼun modèle de régression linéaire avec un processus dʼerreur autocorrélé. On introduit un estimateur linéaire sans biais simple et non paramétrique de la courbe de concentration et de lʼAUC. On montre que cet estimateur construit à partir dʼun plan dʼéchantillonnage régulier approprié est asymptotiquement optimal.
The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with autocorrelated error process. We introduce a simple linear nonparametric unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from an appropriate regular sampling design is asymptotically optimal.
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@article{CRMATH_2012__350_13-14_707_0,
author = {Belouni, Mohamad and Benhenni, Karim},
title = {Plans d'exp\'erience pour l'estimation de la courbe de concentration et de {l'AUC}},
journal = {Comptes Rendus. Math\'ematique},
pages = {707--710},
publisher = {Elsevier},
volume = {350},
number = {13-14},
year = {2012},
doi = {10.1016/j.crma.2012.07.013},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.07.013/}
}
TY - JOUR AU - Belouni, Mohamad AU - Benhenni, Karim TI - Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC JO - Comptes Rendus. Mathématique PY - 2012 SP - 707 EP - 710 VL - 350 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.07.013/ DO - 10.1016/j.crma.2012.07.013 LA - fr ID - CRMATH_2012__350_13-14_707_0 ER -
%0 Journal Article %A Belouni, Mohamad %A Benhenni, Karim %T Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC %J Comptes Rendus. Mathématique %D 2012 %P 707-710 %V 350 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.07.013/ %R 10.1016/j.crma.2012.07.013 %G fr %F CRMATH_2012__350_13-14_707_0
Belouni, Mohamad; Benhenni, Karim. Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC. Comptes Rendus. Mathématique, Tome 350 (2012) no. 13-14, pp. 707-710. doi : 10.1016/j.crma.2012.07.013. http://www.numdam.org/articles/10.1016/j.crma.2012.07.013/
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