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

Author

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  • Jean-Pierre FLORENS
  • Joel L. HOROWITZ
  • Ingrid VAN KEILEGOM

Abstract

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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    File URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.128.0203
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    References listed on IDEAS

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    1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    2. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Florens, Jean-Pierre & Van Bellegem, Sébastien, 2015. "Instrumental variable estimation in functional linear models," Journal of Econometrics, Elsevier, vol. 186(2), pages 465-476.
    4. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    5. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
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    Cited by:

    1. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.

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    More about this item

    Keywords

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

    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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