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Iterative regularization in nonparametric instrumental regression

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  • JOHANNES, Jan

    ()
    (Université catholique de Louvain, Institut de Statistique, de Biostatistique et de Sciences Actuarielles, B-1348 Louvain-la-Neuve, Belgium)

  • VAN BELLEGEM, Sébastien

    ()
    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium and Toulouse School of Economics, F-3000 Toulouse, France)

  • VANHEMS, Anne

    (Toulouse School of Economics and Toulouse Business School, F-3000 Toulouse, France)

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.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010055.

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Date of creation: 01 Sep 2010
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Handle: RePEc:cor:louvco:2010055

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Keywords: nonparametric estimation; instrumental variable; ill-posed inverse problem; iterative method; estimation by projection;

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  1. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  2. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, April.
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Cited by:
  1. 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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