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Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors

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  • Yuanshan Wu
  • Yanyuan Ma
  • Guosheng Yin

Abstract

Censored quantile regression is an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the usual central covariate effects, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treating mismeasured covariates as error-free would result in estimation bias. Under censored quantile regression, we propose smoothed and corrected estimating equations to obtain consistent estimators. We establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients. Compared with the naive estimator, the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions. We conduct simulation studies to examine the finite-sample properties of the new method and apply it to a lung cancer study. Supplementary materials for this article are available online.

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  • 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.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1670-1683
    DOI: 10.1080/01621459.2014.989323
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    Cited by:

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    2. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    4. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    5. 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.
    6. 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.
    7. Zexi Cai & Tony Sit, 2023. "On interquantile smoothness of censored quantile regression with induced smoothing," Biometrics, The International Biometric Society, vol. 79(4), pages 3549-3563, December.

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