Iterative Regularization in Nonparametric Instrumental Regression

Jan Johannes, Sebastien Van Bellegem () and Anne Vanhems ()

No 630, IDEI Working Papers from Institut d'Économie Industrielle (IDEI), Toulouse

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 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.

Keywords: Nonparametric estimation; Instrumental variable; Ill-posed inverse problem (search for similar items in EconPapers)
JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2010-07
New Economics Papers: this item is included in nep-ecm, nep-mic and nep-ore
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Citations: View citations in EconPapers (6)

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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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Persistent link: https://EconPapers.repec.org/RePEc:ide:wpaper:23149

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