Iterative Regularization in Nonparametric Instrumental Regression
AbstractWe 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.
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Bibliographic InfoPaper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 10-184.
Date of creation: 16 Jul 2010
Date of revision:
Nonparametric estimation; Instrumental variable; Ill-posed inverse problem;
Other versions of this item:
- JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2010. "Iterative regularization in nonparametric instrumental regression," CORE Discussion Papers 2010055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," IDEI Working Papers 630, Institut d'Économie Industrielle (IDEI), Toulouse.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-02 (All new papers)
- NEP-ECM-2010-10-02 (Econometrics)
- NEP-ORE-2010-10-02 (Operations Research)
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- Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
- Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
- Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
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