Iterative regularization in nonparametric instrumental regression

Jan Johannes (), Sebastien Van Bellegem () and Anne Vanhems ()
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Jan Johannes: Université catholique de Louvain, Institut de Statistique, de Biostatistique et de Sciences Actuarielles, B-1348 Louvain-la-Neuve, Belgium

No 2010055, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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.

Keywords: nonparametric estimation; instrumental variable; ill-posed inverse problem; iterative method; estimation by projection (search for similar items in EconPapers)
JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2010-09-01
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Iterative regularisation in nonparametric instrumental regression (2013)
Working Paper: Iterative Regularization in Nonparametric Instrumental Regression (2010)
Working Paper: Iterative Regularization in Nonparametric Instrumental Regression (2010)
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