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Corrected-loss estimation for quantile regression with covariate measurement errors

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  • 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
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    File URL: http://hdl.handle.net/10.1093/biomet/ass005
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    References listed on IDEAS

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    1. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    3. 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.
    4. 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.
    5. 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.
    6. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
    7. 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.
    8. 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.
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    Cited by:

    1. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    3. 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.

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