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Uniform confidence bands for nonparametric errors-in-variables regression

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  • Kato, Kengo
  • Sasaki, Yuya

Abstract

This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown, but assume the availability of validation data or repeated measurements on the latent predictor variable. The proposed confidence band builds on the deconvolution kernel estimation and a novel application of the multiplier bootstrap method. We establish asymptotic validity of the proposed confidence band. To our knowledge, this is the first paper to derive asymptotically valid uniform confidence bands for nonparametric errors-in-variables regression.

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  • Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:516-555
    DOI: 10.1016/j.jeconom.2019.05.021
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    Cited by:

    1. Hao Dong & Taisuke Otsu & Luke Taylor, 2023. "Bandwidth selection for nonparametric regression with errors-in-variables," Econometric Reviews, Taylor & Francis Journals, vol. 42(4), pages 393-419, April.
    2. 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.
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    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. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2019. "Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator," Journal of Econometrics, Elsevier, vol. 211(2), pages 507-538.
    6. Hao Dong & Daniel L. Millimet, 2020. "Propensity Score Weighting with Mismeasured Covariates: An Application to Two Financial Literacy Interventions," JRFM, MDPI, vol. 13(11), pages 1-24, November.
    7. Katharina Proksch & Nicolai Bissantz & Hajo Holzmann, 2022. "Simultaneous inference for Berkson errors-in-variables regression under fixed design," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 773-800, August.
    8. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.
    9. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    10. 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.

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    More about this item

    Keywords

    Confidence band; Deconvolution; Errors-in-variables regression; Multiplier bootstrap;
    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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