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Bias-corrected confidence intervals in a class of linear inverse problems

Author

Listed:
  • Jean-Pierre Florens

    (Institute for Fiscal Studies)

  • Joel L. Horowitz

    (Institute for Fiscal Studies and Northwestern University)

  • Ingred van Keilegom

    (Institute for Fiscal Studies)

Abstract

In this paper we propose a novel method to construct confi dence intervals in a class of linear inverse problems. First, point estimators are obtained via a spectral cut-off method depending on a regularisation parameter, that determines the bias of the estimator. Next, the proposed con fidence interval corrects for this bias by explicitly estimating it based on a second regularisation parameter ?, which is asymptotically smaller than a. The coverage error of the interval is shown to converge to zero. The proposed method is illustrated via two simulation studies, one in the context of functional linear regression, and the second one in the context of instrumental regression.

Suggested Citation

  • Jean-Pierre Florens & Joel L. Horowitz & Ingred van Keilegom, 2016. "Bias-corrected confidence intervals in a class of linear inverse problems," CeMMAP working papers CWP19/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:19/16
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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. Cardot, Herve & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," LIDAM Reprints ISBA 2010034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    4. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
    5. Florens, Jean-Pierre & Van Bellegem, Sébastien, 2015. "Instrumental variable estimation in functional linear models," Journal of Econometrics, Elsevier, vol. 186(2), pages 465-476.
    6. 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.
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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; instrumental regression; inverse problem; regularisation; spectral cut-o ff;
    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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