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 , où correspond à la partie non linéaire et X est un vecteur aléatoire prenant ses valeurs dans , il sʼagit alors de construire une procédure de test permettant de vérifier si lʼhypothèse selon laquelle la fonction m peut sʼécrire sous la forme , où les sont des fonctions définie sur , est vraisemblable.
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 , where stands as the nonlinear part and X is a random vector taking values in the space , 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 , where the ʼs are functions defined on .
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@article{CRMATH_2013__351_3-4_143_0, 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}, volume = {351}, number = {3-4}, year = {2013}, doi = {10.1016/j.crma.2013.01.016}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2013.01.016/} }
TY - JOUR AU - Chokri, Khalid AU - Louani, Djamal TI - Additivity test on the nonlinear part in partially linear models JO - Comptes Rendus. Mathématique PY - 2013 SP - 143 EP - 148 VL - 351 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.01.016/ DO - 10.1016/j.crma.2013.01.016 LA - en ID - CRMATH_2013__351_3-4_143_0 ER -
%0 Journal Article %A Chokri, Khalid %A Louani, Djamal %T Additivity test on the nonlinear part in partially linear models %J Comptes Rendus. Mathématique %D 2013 %P 143-148 %V 351 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.01.016/ %R 10.1016/j.crma.2013.01.016 %G en %F CRMATH_2013__351_3-4_143_0
Chokri, Khalid; Louani, Djamal. Additivity test on the nonlinear part in partially linear models. Comptes Rendus. Mathématique, Tome 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/
[1] Estimation and testing in a partial linear regression model under long-memory dependence, Bernoulli, Volume 10 (2004), pp. 49-78
[2] 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] 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] 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] A test for additivity in nonparametric regression, Ann. Inst. Stat. Math., Volume 54 (2002), pp. 60-82
[6] Testing additivity by kernel-based methods: what is a reasonable test?, Bernoulli, Volume 7 (2001), pp. 669-697
[7] Additive prediction and boosting for functional data, Comput. Stat. Data Anal., Volume 53 (2009), pp. 1400-1413
[8] Testing in partial linear regression models with dependent errors, J. Nonparametr. Stat., Volume 15 (2003), pp. 93-111
[9] Testing additivity in generalized nonparametric regression models with estimated parameters, J. Econom., Volume 104 (2001), pp. 1-48
[10] 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] Additive regression and other nonparametric models, Ann. Stat., Volume 13 (1985), pp. 689-705
[13] The oscillation behavior of processes: The multivariate case, Ann. Probab., Volume 12 (1984), pp. 361-379
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