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Nonparametric robust regression estimation for censored data

Author

Listed:
  • Mohamed Lemdani

    (Univ. de Lille 2.)

  • Elias Ould Saïd

    (Univ. Lille Nord de France
    Univ. du Littoral Côte d’Opale, LMPA)

Abstract

In this paper, we consider a robust regression estimator when the interest random variable is subject to random right-censoring. Based on the so-called synthetic data, we define a new kernel estimator. Under classical conditions and using a VC-classes theory, we establish its uniform consistency with rate and asymptotic normality properties. Special cases are studied and simulations are drawn to illustrate the main results.

Suggested Citation

  • Mohamed Lemdani & Elias Ould Saïd, 2017. "Nonparametric robust regression estimation for censored data," Statistical Papers, Springer, vol. 58(2), pages 505-525, June.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0709-8
    DOI: 10.1007/s00362-015-0709-8
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    References listed on IDEAS

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    1. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    2. Indrani Basak, 1992. "Robust regression with censored data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 323-344, April.
    3. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    4. Kohler, Michael & Máthé, Kinga & Pintér, Márta, 2002. "Prediction from Randomly Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 73-100, January.
    5. Carbonez A. & Györfi L. & Meulen E.C. van der, 1995. "Partitioning-Estimates Of A Regression Function Under Random Censoring," Statistics & Risk Modeling, De Gruyter, vol. 13(1), pages 21-38, January.
    6. Boente, Graciela & Rodriguez, Daniela, 2006. "Robust estimators of high order derivatives of regression functions," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1335-1344, July.
    7. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
    8. Jiantao Li & Min Zheng, 2009. "Robust estimation of multivariate regression model," Statistical Papers, Springer, vol. 50(1), pages 81-100, January.
    9. 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.
    10. Einmahl, J.H.J. & Deheuvels, P., 2000. "Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications," Other publications TiSEM ac9bbdc0-62f8-4b48-9a84-1, Tilburg University, School of Economics and Management.
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