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Nonlinear Censored Regression Using Synthetic Data

Author

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  • MICHEL DELECROIX
  • OLIVIER LOPEZ
  • VALENTIN PATILEA

Abstract

. The problem of estimating a nonlinear regression model, when the dependent variable is randomly censored, is considered. The parameter of the model is estimated by least squares using synthetic data. Consistency and asymptotic normality of the least squares estimators are derived. The proofs are based on a novel approach that uses i.i.d. representations of synthetic data through Kaplan–Meier integrals. The asymptotic results are supported by a small simulation study.

Suggested Citation

  • Michel Delecroix & Olivier Lopez & Valentin Patilea, 2008. "Nonlinear Censored Regression Using Synthetic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 248-265, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:248-265
    DOI: 10.1111/j.1467-9469.2007.00591.x
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    Citations

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    Cited by:

    1. Lili Yu & Liang Liu & Ding-Geng(Din) Chen, 2013. "Weighted Least-Squares Method for Right-Censored Data in Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 69(2), pages 358-365, June.
    2. Salah, Khardani & Yousri, Slaoui, 2019. "Nonparametric relative regression under random censorship model," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 116-122.
    3. Zhao, Xiaobing & Zhou, Xian, 2014. "Sufficient dimension reduction on marginal regression for gaps of recurrent events," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 56-71.
    4. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Parametrically guided local quasi-likelihood with censored data," LIDAM Discussion Papers ISBA 2016011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2012. "Guided censored regression," LIDAM Discussion Papers ISBA 2012023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Majda Talamakrouni & Anouar El Ghouch & Ingrid Van Keilegom, 2015. "Guided Censored Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 214-233, March.
    7. Kevin Burke & Valentin Patilea, 2021. "A likelihood-based approach for cure regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 693-712, September.
    8. Mohamed Lemdani & Elias Ould Saïd, 2017. "Nonparametric robust regression estimation for censored data," Statistical Papers, Springer, vol. 58(2), pages 505-525, June.

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