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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 ? + . We consider the case where the density of the measurement error 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 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 is known. Our approximation results are applicable to various contexts, such as con?dence bands for FX ? and its quantiles, and for performing various cdf-based tests such as goodness-of-?t 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.

Suggested Citation

  • Karun Adusumilli & Taisuke Otsu & Yoon-Jae Whang, "undated". "Inference On Distribution Functions Under Measurement Error," Working Paper Series no108, Institute of Economic Research, Seoul National University.
    • Handle: RePEc:snu:ioerwp:no108
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    Cited by:

    1. 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.
    2. Haoze Hou & Wei Huang & Zheng Zhang, 2025. "Non-parametric Quantile Regression and Uniform Inference with Unknown Error Distribution," Papers 2504.01761, arXiv.org.
    3. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On linearization of nonparametric deconvolution estimators for repeated measurements model," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    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. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    6. Mohamed Doukali & Xiaojun Song & Abderrahim Taamouti, 2024. "Value‐at‐Risk under Measurement Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 690-713, June.
    7. 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.
    8. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    9. 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.
    10. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    11. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.
    12. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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