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On the uniform convergence of deconvolution estimators from repeated measurements

Author

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  • Daisuke Kurisu
  • Taisuke Otsu

Abstract

This paper studies the uniform convergence rates of Li and Vuong's (1998) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015) for the classical measurement error model, where repeated measurements are available. Our assumptions are weaker than existing results, such as Li and Vuong (1998) which requires bounded support, and a specialization of Bonhomme and Robin (2010) which requires the existence of moment generating functions of certain observables. Moreover, our uniform convergence rates are typically faster than those obtained in these papers.

Suggested Citation

  • Daisuke Kurisu & Taisuke Otsu, 2019. "On the uniform convergence of deconvolution estimators from repeated measurements," STICERD - Econometrics Paper Series 604, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:604
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    References listed on IDEAS

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    1. Otsu, Taisuke & Taylor, Luke, 2021. "Specification Testing For Errors-In-Variables Models," Econometric Theory, Cambridge University Press, vol. 37(4), pages 747-768, August.
    2. Peter Arcidiacono & Esteban M. Aucejo & Hanming Fang & Kenneth I. Spenner, 2011. "Does affirmative action lead to mismatch? A new test and evidence," Quantitative Economics, Econometric Society, vol. 2(3), pages 303-333, November.
    3. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 491-533.
    4. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    5. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    6. 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.
    7. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60, Elsevier.
    8. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Comte, Fabienne & Kappus, Johanna, 2015. "Density deconvolution from repeated measurements without symmetry assumption on the errors," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 31-46.
    10. Elena Krasnokutskaya, 2011. "Identification and Estimation of Auction Models with Unobserved Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 293-327.
    11. Adusumilli, Karun & Otsu, Taisuke, 2018. "Nonparametric Instrumental Regression With Errors In Variables," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1256-1280, December.
    12. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    13. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
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    Cited by:

    1. Adusumilli, Karun & Kurisu, Daisuke & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," Journal of Econometrics, Elsevier, vol. 215(1), pages 131-164.
    2. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2022. "Estimation of varying coefficient models with measurement error," Journal of Econometrics, Elsevier, vol. 230(2), pages 388-415.
    3. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    4. Adusumilli, Karun & Kurisu, Daisies & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," LSE Research Online Documents on Economics 102692, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    measurement error; deconvolution; uniform convergence;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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