Statistics
Asymptotic results for the linear parameter estimate in partially linear additive regression model
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1105-1109.

In this Note, we study the linear part of the semi-parametric regression model defined by Yi=Ziβ+j=1dmj(Xij)+εi, 1in, where Zi=(Zi1,,Zip), Xi=(Xi1,,Xid) are vectors of explanatory variables, β=(β1,,βp) is a vector of unknown parameters, m1,,md are unknown univariate real functions, and ε1,,εn are independent random modelling errors with mean zero and finite variances. Using the nonparametric kernel technique combined with the marginal integration method to estimate the functions (mj)1jd and the least-square error criterion to estimate the parameter β, we establish the asymptotic normality together with the iterated logarithm law of the estimate βˆ of β.

Cette Note est consacrée à lʼétude de la partie linéaire du modèle de la régression partiellement linéaire défini par Yi=Ziβ+j=1dmj(Xij)+εi, 1in, où Zi=(Zi1,,Zip), Xi=(Xi1,,Xid) sont des vecteurs de variables explicatives, β=(β1,,βp) est un vecteur de paramèters inconnus, m1,,md sont des fonctions réelles univariées inconnues, et ε1,,εn sont les erreurs de modélisation supposées indépendantes de moyennes nulles et de variances finies. En utilisant la méthode du noyau accompagnée de la méthode dʼintégration marginale pour estimer les fonctions (mj)1jd et le critère des moindres carrés pour estimer le paramètre β, nous établissons la normalité asymptotique et la loi du logarithme itéré pour lʼestimateur βˆ de β.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.09.010
Chokri, Khalid 1, 2; Louani, Djamal 1, 2

1 L.S.T.A., Université de Paris 6, 4, place de Jussieu, 75252 Paris cedex 05, France
2 L.S.T.A., Université de Reims, BP 1039, 51687 Reims cedex 2, France
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Chokri, Khalid; Louani, Djamal. Asymptotic results for the linear parameter estimate in partially linear additive regression model. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1105-1109. doi : 10.1016/j.crma.2011.09.010. http://www.numdam.org/articles/10.1016/j.crma.2011.09.010/

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