IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v99y2012i2p405-421.html
   My bibliography  Save this article

Corrected-loss estimation for quantile regression with covariate measurement errors

Author

Listed:
  • Huixia Judy Wang
  • Leonard A. Stefanski
  • Zhongyi Zhu

Abstract

We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered. Copyright 2012, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:405-421
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ass005
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Carroll, Raymond J. & Freedman, Laurence & Pee, David, 1997. "Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models," SFB 373 Discussion Papers 1997,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    4. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    5. 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.
    6. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
    7. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1010-1043, August.
    8. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    9. Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Childhood Intervention," IZA Discussion Papers 13101, Institute of Labor Economics (IZA).
    2. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Child Intervention," CEPR Discussion Papers 14721, C.E.P.R. Discussion Papers.
    3. Damian Clarke & Manuel Llorca Jaña & Daniel Pailañir, 2023. "The use of quantile methods in economic history," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 56(2), pages 115-132, April.
    4. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    5. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    6. Xiaobo Wang & Jiayu Huang & Guosheng Yin & Jian Huang & Yuanshan Wu, 2023. "Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 115-141, January.
    7. Kaul, Abhishek & Koul, Hira L., 2015. "Weighted ℓ1-penalized corrected quantile regression for high dimensional measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 72-91.
    8. Yuanshan Wu & Yanyuan Ma & Guosheng Yin, 2015. "Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1670-1683, December.
    9. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    11. Carlos Lamarche, 2023. "Quantile Regression with an Endogenous Misclassified Binary Regressor," CEDLAS, Working Papers 0318, CEDLAS, Universidad Nacional de La Plata.
    12. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    13. Liqiong Chen & Antonio F. Galvao & Suyong Song, 2021. "Quantile Regression with Generated Regressors," Econometrics, MDPI, vol. 9(2), pages 1-35, April.

    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. Chesher, Andrew, 2017. "Understanding the effect of measurement error on quantile regressions," Journal of Econometrics, Elsevier, vol. 200(2), pages 223-237.
    2. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Childhood Intervention," IZA Discussion Papers 13101, Institute of Labor Economics (IZA).
    3. Yuanshan Wu & Yanyuan Ma & Guosheng Yin, 2015. "Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1670-1683, December.
    4. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Child Intervention," CEPR Discussion Papers 14721, C.E.P.R. Discussion Papers.
    5. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    6. Mittag, Nikolas, 2016. "Correcting for Misreporting of Government Benefits," IZA Discussion Papers 10266, Institute of Labor Economics (IZA).
    7. 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.
    8. Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    9. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Mar 2024.
    10. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    11. Manuel Arellano & Richard Blundell & Stéphane Bonhomme, 2017. "Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework," Econometrica, Econometric Society, vol. 85, pages 693-734, May.
    12. Anil K. Bera & Antonio F. Galvao Jr. & Gabriel V. Montes-Rojas & Sung Y. Park, 2014. "Which Quantile is the Most Informative? Maximum Likelihood, Maximum Entropy and Quantile Regression," World Scientific Book Chapters, in: Kaddour Hadri & William Mikhail (ed.), Econometric Methods and Their Applications in Finance, Macro and Related Fields, chapter 7, pages 167-199, World Scientific Publishing Co. Pte. Ltd..
    13. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    14. Raymond Carroll & Xiaohong Chen & Yingyao Hu, 2010. "Identification and estimation of nonlinear models using two samples with nonclassical measurement errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 419-423.
    15. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    16. Christine Mulhern & Isaac M. Opper, 2021. "Measuring and Summarizing the Multiple Dimensions of Teacher Effectiveness," CESifo Working Paper Series 9263, CESifo.
    17. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.
    18. Schmidt, Christoph M. & Tauchmann, Harald, 2011. "Heterogeneity in the intergenerational transmission of alcohol consumption: A quantile regression approach," Journal of Health Economics, Elsevier, vol. 30(1), pages 33-42, January.
    19. 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.
    20. Manuel Arellano & Stéphane Bonhomme, 2017. "Nonlinear Panel Data Methods for Dynamic Heterogeneous Agent Models," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 471-496, September.

    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:oup:biomet:v:99:y:2012:i:2:p:405-421. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.