Additivity test on the nonlinear part in partially linear models

Khalid Chokri; Djamal Louani

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

Khalid Chokri ¹; Djamal Louani ^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:

Khalid Chokri ¹; Djamal Louani ^{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 = {Khalid Chokri and Djamal Louani},
     title = {Additivity test on the nonlinear part in partially linear models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {143--148},
     publisher = {Elsevier},
     volume = {351},
     number = {3-4},
     year = {2013},
     doi = {10.1016/j.crma.2013.01.016},
     language = {en},
}

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Khalid Chokri; Djamal Louani. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.016/

References
Cited by

[1] G. Aneiros-Pérez; W. González-Manteiga; P. Vieu Estimation and testing in a partial linear regression model under long-memory dependence, Bernoulli, Volume 10 (2004), pp. 49-78

[2] C. Camlong-Viot Vers un test dʼadditivité en régression non paramétrique sous des conditions de mélange, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2001), pp. 1105-1109

[3] K. Chokri; D. Louani Asymptotic results for the linear parameter estimate in partially linear additive regression model, C. R. Acad. Sci. Paris, Ser. I, Volume 333 (2011), pp. 877-880

[4] L. Delsol; F. Ferraty; P. Vieu Structural tests in regression on functional variable, Recent Advances in Functional Data Analysis and Related Topics, Physica-Verlag/Springer, Heidelberg, Germany, 2011, pp. 77-83

[5] S. Derbort; H. Dette; A. Munk A test for additivity in nonparametric regression, Ann. Inst. Stat. Math., Volume 54 (2002), pp. 60-82

[6] H. Dette; C. von Lieres und Wilkau Testing additivity by kernel-based methods: what is a reasonable test?, Bernoulli, Volume 7 (2001), pp. 669-697

[7] F. Ferraty; P. Vieu Additive prediction and boosting for functional data, Comput. Stat. Data Anal., Volume 53 (2009), pp. 1400-1413

[8] W. González-Manteiga; G. Aneiros-Pérez Testing in partial linear regression models with dependent errors, J. Nonparametr. Stat., Volume 15 (2003), pp. 93-111

[9] P. Gozalo; O. Linton Testing additivity in generalized nonparametric regression models with estimated parameters, J. Econom., Volume 104 (2001), pp. 1-48

[10] N. Li; X. Xu; P. Jin Testing the linearity in partially linear models, J. Nonparametr. Stat., Volume 23 (2011), pp. 99-114

[11] H.G. Müller, F. Yao, Functional additive models, Technical Report, 2008.

[12] C.J. Stone Additive regression and other nonparametric models, Ann. Stat., Volume 13 (1985), pp. 689-705

[13] W. Stute The oscillation behavior of processes: The multivariate case, Ann. Probab., Volume 12 (1984), pp. 361-379

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