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Consistent Density Deconvolution under Partially Known Error Distribution

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  • Schwarz, Maik
  • Van Bellegem, Sébastien

Abstract

We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a simple condition in the time domain. A minimum distance estimator is shown to be consistent imposing only a slightly stronger assumption than the identification condition.

Suggested Citation

  • Schwarz, Maik & Van Bellegem, Sébastien, 2009. "Consistent Density Deconvolution under Partially Known Error Distribution," TSE Working Papers 09-097, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:22200
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    References listed on IDEAS

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    1. Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
    2. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(3), pages 522-545, June.
    3. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    4. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
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    Cited by:

    1. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    3. Aurélie Bertrand & Ingrid Van Keilegom & Catherine Legrand, 2019. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," Biometrics, The International Biometric Society, vol. 75(1), pages 297-307, March.
    4. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," IDEI Working Papers 625, Institut d'Économie Industrielle (IDEI), Toulouse.
    5. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    6. Kneip, A. & Simar, L. & Van Keilegom I., 2010. "Boundary estimation in the presence of measurement error with unknown variance," LIDAM Discussion Papers ISBA 2010046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    8. Zhuan Pei & Yi Shen, 2017. "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable," Advances in Econometrics, in: Matias D. Cattaneo & Juan Carlos Escanciano (ed.), Regression Discontinuity Designs, volume 38, pages 455-502, Emerald Publishing Ltd.
    9. Bertrand, Aurelie & Van Keilegom, Ingrid & Legrand, Catherine, 2017. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," LIDAM Discussion Papers ISBA 2017025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Martin Kroll, 2019. "Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 961-990, November.
    11. Jochmans, Koen & Henry, Marc & Salanié, Bernard, 2017. "Inference On Two-Component Mixtures Under Tail Restrictions," Econometric Theory, Cambridge University Press, vol. 33(3), pages 610-635, June.

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    Keywords

    deconvolution; error measurement; density estimation;
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