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Parametric modeling of quantile regression coefficient functions with censored and truncated data

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  • Paolo Frumento
  • Matteo Bottai

Abstract

Quantile regression coefficient functions describe how the coefficients of a quantile regression model depend on the order of the quantile. A method for parametric modeling of quantile regression coefficient functions was discussed in a recent article. The aim of the present work is to extend the existing framework to censored and truncated data. We propose an estimator and derive its asymptotic properties. We discuss goodness‐of‐fit measures, present simulation results, and analyze the data that motivated this article. The described estimator has been implemented in the R package qrcm.

Suggested Citation

  • Paolo Frumento & Matteo Bottai, 2017. "Parametric modeling of quantile regression coefficient functions with censored and truncated data," Biometrics, The International Biometric Society, vol. 73(4), pages 1179-1188, December.
    • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1179-1188
    DOI: 10.1111/biom.12675
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    References listed on IDEAS

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    1. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    3. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2012. "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 481-498, May.
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    Cited by:

    1. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    2. Paolo Frumento & Matteo Bottai & Iv'an Fern'andez-Val, 2020. "Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data," Papers 2006.00160, arXiv.org.
    3. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    4. Hao, Meiling & Lin, Yuanyuan & Shen, Guohao & Su, Wen, 2023. "Nonparametric inference on smoothed quantile regression process," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. E. Fusco & R. Benedetti & F. Vidoli, 2023. "Stochastic frontier estimation through parametric modelling of quantile regression coefficients," Empirical Economics, Springer, vol. 64(2), pages 869-896, February.
    6. Zhiyuan Zuo & Liang Wang & Yuhlong Lio, 2022. "Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations," Energies, MDPI, vol. 16(1), pages 1-25, December.
    7. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    8. Viviana Carcaiso & Leonardo Grilli, 2023. "Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1061-1082, October.
    9. Paolo Frumento & Nicola Salvati, 2020. "Parametric modelling of M‐quantile regression coefficient functions with application to small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 229-250, January.
    10. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).

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