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On Deconvolution as a First Stage Nonparametric Estimator

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  • Yingyao Hu
  • Geert Ridder

Abstract

We reconsider Taupin's (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to a class of distributions with restricted support, then much weaker smoothness assumptions than hers suffice to ensure [image omitted] consistency of the estimator. In addition, we show that the INLR estimator remains consistent under these weaker smoothness assumptions if the support of the measurement error distribution expands with the sample size. In that case the estimator remains also asymptotically normal with a rate of convergence that is arbitrarily close to [image omitted]. Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.

Suggested Citation

  • Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
  • Handle: RePEc:taf:emetrv:v:29:y:2010:i:4:p:365-396
    DOI: 10.1080/07474930903559276
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    References listed on IDEAS

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    1. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    2. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    3. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366.
    4. Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 145-168.
    5. 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.
    6. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
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    Cited by:

    1. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    2. repec:eee:econom:v:200:y:2017:i:1:p:48-58 is not listed on IDEAS
    3. Susanne M. Schennach, 2013. "Convolution without independence," CeMMAP working papers CWP46/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Irene Botosaru, 2017. "Identifying Distributions in a Panel Model with Heteroskedasticity: An Application to Earnings Volatility," Discussion Papers dp17-11, Department of Economics, Simon Fraser University.

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