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Additivity test on the nonlinear part in partially linear models
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 143-148.

Our aim in this Note is to build an additivity test relative to the nonlinear part of the partially linear model. More precisely, considering the model of the form Y=Zβ+m(X)+ε, where m(X) stands as the nonlinear part and X is a random vector taking values in the space Rd, our goal is to construct a testing procedure that allows us to test the validity of the hypothesis according to which the function m may be written with the shape m(x)=l=1dml(xl), where the mlʼs are functions defined on R.

Cette Note a pour objet de construire un test dʼadditivité de la partie non linéaire du modèle partiellement linéaire. Plus précisément, en considérant un modèle de la forme Y=Zβ+m(X)+ε, où m(X) correspond à la partie non linéaire et X est un vecteur aléatoire prenant ses valeurs dans Rd, il sʼagit alors de construire une procédure de test permettant de vérifier si lʼhypothèse selon laquelle la fonction m peut sʼécrire sous la forme m(x)=l=1dml(xl), où les mi sont des fonctions définie sur R, est vraisemblable.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.01.016
Chokri, Khalid 1; Louani, Djamal 1, 2

1 LSTA, université Paris-6, 175, rue du Chevaleret, 75013 Paris, France
2 Université de Reims–Champagne–Ardennes, BP 1039, 51687 Reims cedex 2, France
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Chokri, Khalid; Louani, Djamal. Additivity test on the nonlinear part in partially linear models. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 143-148. doi : 10.1016/j.crma.2013.01.016. http://www.numdam.org/articles/10.1016/j.crma.2013.01.016/

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