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Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

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  • Xiaowen Liang

    (Harbin Institute of Technology)

  • Boping Tian

    (Harbin Institute of Technology)

Abstract

In this paper, we consider quantile regression estimation for linear models with covariate measurement errors and nonignorable missing responses. Firstly, the influence of measurement errors is eliminated through the bias-corrected quantile loss function. To handle the identifiability issue in the nonignorable missing, a nonresponse instrument is used. Then, based on the inverse probability weighting approach, we propose a weighted bias-corrected quantile loss function that can handle both nonignorable missingness and covariate measurement errors. Under certain regularity conditions, we establish the asymptotic properties of the proposed estimators. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.

Suggested Citation

  • Xiaowen Liang & Boping Tian, 2025. "Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(4), pages 523-549, May.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:4:d:10.1007_s00184-024-00967-z
    DOI: 10.1007/s00184-024-00967-z
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Puying Zhao & Hui Zhao & Niansheng Tang & Zhaohai Li, 2017. "Weighted composite quantile regression analysis for nonignorable missing data using nonresponse instrument," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 189-212, April.
    3. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. repec:mpr:mprres:8160 is not listed on IDEAS
    6. Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.
    7. 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.
    8. 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.
    9. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346, September.
    10. Ji Chen & Jun Shao & Fang Fang, 2021. "Instrument search in pseudo-likelihood approach for nonignorable nonresponse," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 519-533, June.
    11. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    12. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2018. "Weighted composite quantile regression for partially linear varying coefficient models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 3987-4005, August.
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