Iterative Regularization in Nonparametric Instrumental Regression

Johannes, Jan, Van Bellegem, Sébastien and Vanhems, Anne (2010) Iterative Regularization in Nonparametric Instrumental Regression. TSE Working Paper, n. 10-184, Toulouse

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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.

Item Type: Monograph (Working Paper)
Language: English
Date: 16 July 2010
Place of Publication: Toulouse
Uncontrolled Keywords: Nonparametric estimation, Instrumental variable, Ill-posed inverse problem
JEL codes: C14 - Semiparametric and Nonparametric Methods
C30 - General
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 18 Jan 2012 06:02
Last Modified: 19 Mar 2018 15:41

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