IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v29y2017i2p301-325.html
   My bibliography  Save this article

An alternative local polynomial estimator for the error-in-variables problem

Author

Listed:
  • Xianzheng Huang
  • Haiming Zhou

Abstract

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle et al. [(2009), ‘A Design-adaptive Local Polynomial Estimator for the Errors-in-variables Problem’, Journal of the American Statistical Association, 104, 348–359] as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable.

Suggested Citation

  • Xianzheng Huang & Haiming Zhou, 2017. "An alternative local polynomial estimator for the error-in-variables problem," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 301-325, April.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:301-325
    DOI: 10.1080/10485252.2017.1303060
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2017.1303060
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2017.1303060?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    2. 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.
    3. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    2. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Hao Dong & Taisuke Otsu & Luke Taylor, 2022. "Nonparametric estimation of additive models with errors-in-variables," Econometric Reviews, Taylor & Francis Journals, vol. 41(10), pages 1164-1204, November.
    4. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2009. "Nonparametric Prediction in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 993-1003.
    5. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    6. Hao Dong & Taisuke Otsu, 2018. "Nonparametric Estimation of Additive Model With Errors-in-Variables," Departmental Working Papers 1812, Southern Methodist University, Department of Economics.
    7. Julie McIntyre & Brent A. Johnson & Stephen M. Rappaport, 2018. "Monte Carlo methods for nonparametric regression with heteroscedastic measurement error," Biometrics, The International Biometric Society, vol. 74(2), pages 498-505, June.
    8. Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    9. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    10. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    11. Huijun Guo & Youming Liu, 2019. "Regression estimation under strong mixing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 553-576, June.
    12. Mittag, Nikolas, 2016. "Correcting for Misreporting of Government Benefits," IZA Discussion Papers 10266, Institute of Labor Economics (IZA).
    13. Marco Di Marzio & Stefania Fensore & Charles C. Taylor, 2023. "Kernel regression for errors-in-variables problems in the circular domain," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1217-1237, October.
    14. Stoker, Thomas M. & Berndt, Ernst R. & Denny Ellerman, A. & Schennach, Susanne M., 2005. "Panel data analysis of U.S. coal productivity," Journal of Econometrics, Elsevier, vol. 127(2), pages 131-164, August.
    15. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    16. Battistin, Erich & Chesher, Andrew, 2014. "Treatment effect estimation with covariate measurement error," Journal of Econometrics, Elsevier, vol. 178(2), pages 707-715.
    17. Christoph T. Weiss, 2012. "Persistent Attitudes and Behaviors," "Marco Fanno" Working Papers 0143, Dipartimento di Scienze Economiche "Marco Fanno".
    18. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    19. Susanne M. Schennach & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification of the classical errors-in-variables model without side information," Boston College Working Papers in Economics 674, Boston College Department of Economics.
    20. Attanasio, Orazio & Cattan, Sarah & Fitzsimons, Emla & Meghir, Costas & Rubio-Codina, Marta, 2015. "Estimating the Production Function for Human Capital: Results from a Randomized Control Trial in Colombia," IZA Discussion Papers 8856, Institute of Labor Economics (IZA).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:301-325. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.