期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2010
卷号：2010
期号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：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 ill-posed 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
