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Multiple imputation in quantile regression

Author

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  • Ying Wei
  • Yanyuan Ma
  • Raymond J. Carroll

Abstract

We propose a multiple imputation estimator for parameter estimation in a quantile regression model when some covariates are missing at random. The estimation procedure fully utilizes the entire dataset to achieve increased efficiency, and the resulting coefficient estimators are root-n consistent and asymptotically normal. To protect against possible model misspecification, we further propose a shrinkage estimator, which automatically adjusts for possible bias. The finite sample performance of our estimator is investigated in a simulation study. Finally, we apply our methodology to part of the Eating at American's Table Study data, investigating the association between two measures of dietary intake. Copyright 2012, Oxford University Press.

Suggested Citation

  • Ying Wei & Yanyuan Ma & Raymond J. Carroll, 2012. "Multiple imputation in quantile regression," Biometrika, Biometrika Trust, vol. 99(2), pages 423-438.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:423-438
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    File URL: http://hdl.handle.net/10.1093/biomet/ass007
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    Citations

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    Cited by:

    1. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    2. Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    3. Harding, Matthew & Lamarche, Carlos, 2019. "A panel quantile approach to attrition bias in Big Data: Evidence from a randomized experiment," Journal of Econometrics, Elsevier, vol. 211(1), pages 61-82.
    4. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    5. Tonghui Yu & Liming Xiang & Huixia Judy Wang, 2021. "Quantile regression for survival data with covariates subject to detection limits," Biometrics, The International Biometric Society, vol. 77(2), pages 610-621, June.
    6. Cheng, Hao, 2021. "Importance sampling imputation algorithms in quantile regression with their application in CGSS data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 498-508.
    7. Sherwood, Ben, 2016. "Variable selection for additive partial linear quantile regression with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 206-223.
    8. Figueiredo, Erik & Lima, Luiz Renato & Orefice, Gianluca, 2020. "Migration, trade and spillover effects," Journal of Comparative Economics, Elsevier, vol. 48(2), pages 405-421.
    9. Shuanghua Luo & Changlin Mei & Cheng-yi Zhang, 2017. "Smoothed empirical likelihood for quantile regression models with response data missing at random," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 95-116, January.
    10. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    11. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    12. Xuerong Chen & Alan T. K. Wan & Yong Zhou, 2015. "Efficient Quantile Regression Analysis With Missing Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 723-741, June.
    13. Stephen S. M. Lee & Mehdi Soleymani, 2015. "A Simple Formula for Mixing Estimators With Different Convergence Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1463-1478, December.
    14. Hao Cheng & Ying Wei, 2018. "A fast imputation algorithm in quantile regression," Computational Statistics, Springer, vol. 33(4), pages 1589-1603, December.
    15. Hu, Yanan & Yang, Yaqi & Wang, Chunyu & Tian, Maozai, 2017. "Imputation in nonparametric quantile regression with complex data," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 120-130.
    16. Sun, Jing & Sun, Qihang, 2015. "An improved and efficient estimation method for varying-coefficient model with missing covariates," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 296-303.

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