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Bias-Corrected Confidence Intervals in a Class of Linear Inverse Problems


  • Jean-Pierre FLORENS
  • Joel L. HOROWITZ


We propose a new method for constructing confidence intervals in a class of linear inverse problems. Point estimators are obtained via a spectral cutoff method that depends on a regularization parameter a that determines the bias of the estimator. The proposed confidence interval corrects for this bias by explicitly estimating it based on a second regularization parameter ? that is asymptotically smaller than a. The coverage error of the resulting confidence interval is shown to converge to zero. The proposed method is illustrated by two simulation studies, one in the context of functional linear regression and the other in the context of nonparametric instrumental variables estimation.

Suggested Citation

  • Jean-Pierre FLORENS & Joel L. HOROWITZ & Ingrid VAN KEILEGOM, 2017. "Bias-Corrected Confidence Intervals in a Class of Linear Inverse Problems," Annals of Economics and Statistics, GENES, issue 128, pages 203-228.
  • Handle: RePEc:adr:anecst:y:2017:i:128:p:203-228 DOI: 10.15609/annaeconstat2009.128.0203

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    References listed on IDEAS

    1. Sokullu, Senay, 2016. "Network effects in the German magazine industry," Economics Letters, Elsevier, vol. 143(C), pages 77-79.
    2. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    5. Qi Li & Jeffrey Scott Racine, 2006. "Density Estimation, from Nonparametric Econometrics: Theory and Practice," Introductory Chapters,in: Nonparametric Econometrics: Theory and Practice Princeton University Press.
    6. repec:cup:etheor:v:33:y:2017:i:04:p:839-873_00 is not listed on IDEAS
    7. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(04), pages 839-873, August.
    8. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
    9. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, Department of Economics, University of Bristol, UK.
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    More about this item


    Bias-Correction; Functional Linear Regression; Nonparametric Instrumental Variables; Inverse Problem; Regularization; Spectral Cutoff.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation


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