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Inference on distribution functions under measurement error

Author

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  • Karun Adusumilli
  • Taisuke Otsu
  • Yoon-Jae Whang

Abstract

This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X=X∗+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗. We allow the density of ϵ to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ϵ is known. Our approximation results are applicable to various contexts, such as confidence bands for FX∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X∗, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.
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Suggested Citation

  • Karun Adusumilli & Taisuke Otsu & Yoon-Jae Whang, 2017. "Inference on distribution functions under measurement error," STICERD - Econometrics Paper Series 594, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:594
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    References listed on IDEAS

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    11. 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.
    12. 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.
    13. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.
    14. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1046-1093, December.
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    16. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    17. Hu, Yingyao & Sasaki, Yuya, 2015. "Closed-form estimation of nonparametric models with non-classical measurement errors," Journal of Econometrics, Elsevier, vol. 185(2), pages 392-408.
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    Cited by:

    1. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    2. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On linearization of nonparametric deconvolution estimators for repeated measurements model," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.
    4. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On the uniform convergence of deconvolution estimators from repeated measurements," LSE Research Online Documents on Economics 107533, London School of Economics and Political Science, LSE Library.
    5. Hao Dong & Yuya Sasaki, 2022. "Estimation of average derivatives of latent regressors: with an application to inference on buffer-stock saving," Departmental Working Papers 2204, Southern Methodist University, Department of Economics.
    6. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On linearization of nonparametric deconvolution estimators for repeated measurements model," LSE Research Online Documents on Economics 112676, London School of Economics and Political Science, LSE Library.
    7. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    8. Daisuke Kurisu & Taisuke Otsu, 2021. "On linearization of nonparametric deconvolution estimators for repeated measurements model," STICERD - Econometrics Paper Series 615, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.

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    More about this item

    Keywords

    Measurement error; Confidence band; Stochastic dominance;
    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

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