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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 an 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, 2010. "Consistent density deconvolution under partially known error distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 236-241, February.
  • Handle: RePEc:eee:stapro:v:80:y:2010:i:3-4:p:236-241
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    References listed on IDEAS

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    1. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    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(03), pages 522-545, June.
    3. 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.
    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. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    2. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," TSE Working Papers 10-179, Toulouse School of Economics (TSE).
    3. 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: Regression Discontinuity Designs, volume 38, pages 455-502 Emerald Publishing Ltd.
    4. 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.

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