Article dans une série de papiers de travail :

Jan Johannes, Sébastien Van Bellegem et Anne Vanhems, « Iterative Regularization in Nonparametric Instrumental Regression », TSE Working Paper, n°10-184, 16 juillet 2010.
[ Texte complet ]

Résumé

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an illposed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.

Mots clefs

Nonparametric estimation; Instrumental variable; Ill-posed inverse problem

Codes JEL

C14 : Semiparametric and Nonparametric Methods
C30 : General

Groupe de recherche TSE

Econométrie et statistique