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Iterative regularisation in nonparametric instrumental regression

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  • JOHANNES, Jan
  • VAN BELLEGEM, Sébastien
  • VANHEMS, Anne

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.
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Suggested Citation

  • JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2013. "Iterative regularisation in nonparametric instrumental regression," LIDAM Reprints CORE 2442, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2442
    DOI: 10.1016/j.jspi.2012.07.010
    Note: In : Journal of Statistical Planning and Inference, 143(1), 24-39, 2013
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    Cited by:

    1. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    2. Emir Malikov & Shunan Zhao & Subal C. Kumbhakar, 2020. "Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 457-480, June.
    3. Vanhems, Anne & Van Keilegom, Ingrid, 2019. "Estimation Of A Semiparametric Transformation Model In The Presence Of Endogeneity," Econometric Theory, Cambridge University Press, vol. 35(1), pages 73-110, February.
    4. Bréchet, Thierry & Jouvet, Pierre-André & Rotillon, Gilles, 2013. "Tradable pollution permits in dynamic general equilibrium: Can optimality and acceptability be reconciled?," Ecological Economics, Elsevier, vol. 91(C), pages 89-97.
    5. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," TSE Working Papers 10-184, Toulouse School of Economics (TSE).
    6. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    7. Asin, Nicolas & Johannes, Jan, 2016. "Adaptive non-parametric instrumental regression in the presence of dependence," LIDAM Discussion Papers ISBA 2016015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    9. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    10. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    11. De Monte Enrico, 2024. "Nonparametric Instrumental Regression with Two-Way Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 49-66, January.
    12. Jean-Pierre Florens & Elia Lapenta, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.

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    JEL classification:

    • 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

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