Additivity test on the nonlinear part in partially linear models

Chokri, Khalid; Louani, Djamal

doi:10.1016/j.crma.2013.01.016

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Additivity test on the nonlinear part in partially linear models

Presented by: Paul Deheuvels

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

Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 143-148.

Abstract
Résumé

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 $Y = Z^{⊤} β + m (X) + ε$ , where $m (X)$ stands as the nonlinear part and X is a random vector taking values in the space $R^{d}$ , 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 $m (x) = \sum_{l = 1}^{d} m_{l} (x_{l})$ , where the $m_{l}$ ʼs 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 $Y = Z^{⊤} β + m (X) + ε$ , où $m (X)$ correspond à la partie non linéaire et X est un vecteur aléatoire prenant ses valeurs dans $R^{d}$ , il sʼagit alors de construire une procédure de test permettant de vérifier si lʼhypothèse selon laquelle la fonction m peut sʼécrire sous la forme $m (x) = \sum_{l = 1}^{d} m_{l} (x_{l})$ , où les $m_{i}$ sont des fonctions définie sur $R$ , est vraisemblable.

Received: 2011-12-20
Accepted: 2013-01-31
Published online: 2013-02-01

DOI: 10.1016/j.crma.2013.01.016

Author's affiliations:

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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     author = {Chokri, Khalid and Louani, Djamal},
     title = {Additivity test on the nonlinear part in partially linear models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {143--148},
     publisher = {Elsevier},
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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. https://www.numdam.org/articles/10.1016/j.crma.2013.01.016/

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