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Bandwidth Selection for Nonparametric Regression with Errors-in-Variables

Author

Listed:
  • Hao Dong

    (Southern Methodist University)

  • Taisuke Otsu

    (London School of Economics and Political Science)

  • Luke Taylor

    (Aarhus University)

Abstract

We propose two novel bandwidth selection procedures for the nonparametric regression model with classical measurement error in the regressors. Each method is based on evaluating the prediction errors of the regression using a second (density) deconvolution. The first approach uses a typical leave-one-out cross validation criterion, while the second applies a bootstrap approach and the concept of out-of-bag prediction. We show the asymptotic validity of both procedures and compare them to the SIMEX method of Delaigle and Hall (2008) in a Monte Carlo study. As well as enjoying advantages in terms of computational cost, the methods proposed in this paper lead to lower mean integrated squared error compared to the current state-of-the-art.

Suggested Citation

  • Hao Dong & Taisuke Otsu & Luke Taylor, 2021. "Bandwidth Selection for Nonparametric Regression with Errors-in-Variables," Departmental Working Papers 2104, Southern Methodist University, Department of Economics.
    • Handle: RePEc:smu:ecowpa:2104
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    References listed on IDEAS

    as
    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Davezies, Laurent & Le Barbanchon, Thomas, 2017. "Regression discontinuity design with continuous measurement error in the running variable," Journal of Econometrics, Elsevier, vol. 200(2), pages 260-281.
    3. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
    4. Blattman, Christopher & Jamison, Julian & Koroknay-Palicz, Tricia & Rodrigues, Katherine & Sheridan, Margaret, 2016. "Measuring the measurement error: A method to qualitatively validate survey data," Journal of Development Economics, Elsevier, vol. 120(C), pages 99-112.
    5. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    6. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    7. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    8. 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.
    9. Otávio Bartalotti & Quentin Brummet & Steven Dieterle, 2021. "A Correction for Regression Discontinuity Designs With Group-Specific Mismeasurement of the Running Variable," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 833-848, July.
    10. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, 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. Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    14. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
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    More about this item

    Keywords

    Bandwidth selection; nonparametric regression; deconvolution; classical measurement error.;
    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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