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Inference on distribution functions under measurement error

Author

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  • Adusumilli, Karun
  • Kurisu, Daisies
  • Otsu, Taisuke
  • Whang, Yoon-Jae

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.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:102692
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    References listed on IDEAS

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    1. 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.
    2. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    3. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
    4. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1046-1093, December.
    5. 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.
    6. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    7. Nicolai Bissantz & Lutz Dümbgen & Hajo Holzmann & Axel Munk, 2007. "Non‐parametric confidence bands in deconvolution density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 483-506, June.
    8. Bassett, Gilbert W. & Koenker, Roger W., 1986. "Strong Consistency of Regression Quantiles and Related Empirical Processes," Econometric Theory, Cambridge University Press, vol. 2(2), pages 191-201, August.
    9. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    10. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 19-47, March.
    11. Aurore Delaigle & Peter Hall & Farshid Jamshidi, 2015. "Confidence bands in non-parametric errors-in-variables regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 149-169, January.
    12. 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.
    13. Bissantz, Nicolai & Dümbgen, Lutz & Holzmann, Hajo & Munk, Axel, 2007. "Nonparametric confidence bands in deconvolution density estimation," Technical Reports 2007,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. 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.
    15. 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.
    16. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.
    17. Bert Van Es & Hae‐Won Uh, 2005. "Asymptotic Normality of Kernel‐Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483, September.
    18. Delaigle, Aurore & Hall, Peter, 2006. "On optimal kernel choice for deconvolution," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1594-1602, September.
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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. 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.
    3. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    4. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On linearization of nonparametric deconvolution estimators for repeated measurements model," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. 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.
    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.

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    More about this item

    Keywords

    measurement error; deconvolution; confidence band; stochastic dominance;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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