[Un test d'adéquation nonparamétrique pour la régression]
Dans le cadre de la régression univariée, nous proposons un outil nonparamétrique général permettant de tester si une fonction connue m est un bon candidat pour la fonction de régression au vu des données. Ce test est basé sur la longueur maximale des suites ordonnées (par rapport à la covariable) des résidus de même signe. Aucune hypothèse n'est faite sur l'homoscédasticité des erreurs. De plus, ce test ne nécessite pas la présence de données répétées. Nous donnons ici la loi de la statistique test sous l'hypothèse nulle que la fonction considérée m est la vraie fonction de régression ainsi que sous une certaine classe d'hypothèses alternatives.
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residual plots are useful but heuristic. We introduce a formal statistical test supplementing the graphical analysis. Technically, the test statistic is the maximum length of the sequences of ordered (with respect to the covariate) observations that are consecutively overestimated or underestimated by the candidate regression function. Note that the testing procedure can cope with heteroscedastic errors and no replicates. Recursive formulae allowing one to calculate the exact distribution of the test statistic under the null hypothesis and under a class of alternative hypotheses are given.
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@article{CRMATH_2011__349_3-4_215_0,
author = {Aubin, Jean-Baptiste and Leoni-Aubin, Samuela},
title = {A nonparametric lack-of-fit test for heteroscedastic regression models},
journal = {Comptes Rendus. Math\'ematique},
pages = {215--217},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.12.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.12.009/}
}
TY - JOUR AU - Aubin, Jean-Baptiste AU - Leoni-Aubin, Samuela TI - A nonparametric lack-of-fit test for heteroscedastic regression models JO - Comptes Rendus. Mathématique PY - 2011 SP - 215 EP - 217 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.12.009/ DO - 10.1016/j.crma.2010.12.009 LA - en ID - CRMATH_2011__349_3-4_215_0 ER -
%0 Journal Article %A Aubin, Jean-Baptiste %A Leoni-Aubin, Samuela %T A nonparametric lack-of-fit test for heteroscedastic regression models %J Comptes Rendus. Mathématique %D 2011 %P 215-217 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.12.009/ %R 10.1016/j.crma.2010.12.009 %G en %F CRMATH_2011__349_3-4_215_0
Aubin, Jean-Baptiste; Leoni-Aubin, Samuela. A nonparametric lack-of-fit test for heteroscedastic regression models. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 215-217. doi : 10.1016/j.crma.2010.12.009. http://www.numdam.org/articles/10.1016/j.crma.2010.12.009/
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