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An Adapted Loss Function for Censored Quantile Regression

Author

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  • Mickaël De Backer
  • Anouar El Ghouch
  • Ingrid Van Keilegom

Abstract

In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called “check” function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function the proposed methodology opens the gate to numerous parametric, semiparametric, and nonparametric modeling techniques. To illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency and asymptotic normality of the estimator for linear regression are obtained using several recent results on nonsmooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator. Supplementary materials for this article are available online.

Suggested Citation

  • Mickaël De Backer & Anouar El Ghouch & Ingrid Van Keilegom, 2019. "An Adapted Loss Function for Censored Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1126-1137, July.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:527:p:1126-1137
    DOI: 10.1080/01621459.2018.1469996
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    Cited by:

    1. Mercedes Conde‐Amboage & Ingrid Van Keilegom & Wenceslao González‐Manteiga, 2021. "A new lack‐of‐fit test for quantile regression with censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 655-688, June.
    2. Yue Zhao & Ingrid Van Keilegom & Shanshan Ding, 2022. "Envelopes for censored quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1562-1585, December.
    3. Mickaël De Backer & Anouar El Ghouch & Ingrid Van Keilegom, 2020. "Linear censored quantile regression: A novel minimum‐distance approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1275-1306, December.
    4. Gabriela M. Rodrigues & Edwin M. M. Ortega & Gauss M. Cordeiro & Roberto Vila, 2023. "Quantile Regression with a New Exponentiated Odd Log-Logistic Weibull Distribution," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    5. Jad Beyhum & Lorenzo Tedesco & Ingrid Van Keilegom, 2022. "Instrumental variable quantile regression under random right censoring," Papers 2209.01429, arXiv.org, revised Feb 2023.

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