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Tikhonov Regularization for Functional Minimum Distance Estimators

Author

Listed:
  • P. Gagliardini

    (University of Lugano and Swiss Finance Institute)

  • O. Scaillet

    (University of Geneva and Swiss Finance Institute)

Abstract

We study the asymptotic properties of a Tikhonov Regularized (TiR) estimator of a functional parameter based on a minimum distance principle for nonparametric conditional moment restrictions. The estimator is computationally tractable and takes a closed form in the linear case. We derive its asymptotic Mean Integrated Squared Error (MISE), its rate of convergence and its pointwise asymptotic normality under a regularization parameter depending on sample size. The optimal value of the regularization parameter is characterized. We illustrate our theoretical findings and the small sample properties with simulation results for two numerical examples. We also discuss two data driven selection procedures of the regularization parameter via a spectral representation and a subsampling approximation of the MISE. Finally, we provide an empirical application to nonparametric estimation of an Engel curve.

Suggested Citation

  • P. Gagliardini & O. Scaillet, 2006. "Tikhonov Regularization for Functional Minimum Distance Estimators," Swiss Finance Institute Research Paper Series 06-30, Swiss Finance Institute, revised Nov 2006.
    • Handle: RePEc:chf:rpseri:rp0630
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    Cited by:

    1. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(3), pages 497-521, June.
    2. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    3. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(3), pages 472-496, June.
    4. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    5. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    6. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.

    More about this item

    Keywords

    MinimumDistance; Nonparametric Estimation; III-posed In-verse Problems; Tikhonov Regularization; Endogeneity; InstrumentalVariable; Generalized Method of Moments; Subsampling; Engelcurve.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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