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Local linear estimation of the regression function for twice censored data

Author

Listed:
  • Ouafae Benrabah

    (Université du Littoral Cote d’Opale (ULCO), Laboratoire de Mathématiques pures et appliquées (LMPA))

  • Feriel Bouhadjera

    (Université du Littoral Cote d’Opale (ULCO), Laboratoire de Mathématiques pures et appliquées (LMPA)
    Université Badji Mokhtar Annaba (UBMA), Laboratoire de Probabilits et Statistique (LaPS))

  • Elias Ould Saïd

    (Université du Littoral Cote d’Opale (ULCO), Laboratoire de Mathématiques pures et appliquées (LMPA)
    IUT de Calais)

Abstract

This paper is concerned with a nonparametric estimator of the regression function based on the local linear estimation method in a twice censoring setting. The proposed method avoid the problem of boundary effect and reduces the bias term. Under suitable assumptions, the strong uniform almost sure consistency with rate is established and the finite sample properties of the local linear regression smoother is investigated by means of a simulation study.

Suggested Citation

  • Ouafae Benrabah & Feriel Bouhadjera & Elias Ould Saïd, 2022. "Local linear estimation of the regression function for twice censored data," Statistical Papers, Springer, vol. 63(2), pages 489-514, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01240-5
    DOI: 10.1007/s00362-021-01240-5
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    References listed on IDEAS

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    1. Demongeot, Jacques & Hamie, Ali & Laksaci, Ali & Rachdi, Mustapha, 2016. "Relative-error prediction in nonparametric functional statistics: Theory and practice," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 261-268.
    2. Messaci, Fatiha & Nemouchi, Nahima, 2011. "A law of the iterated logarithm for the product limit estimator with doubly censored data," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1241-1244, August.
    3. Pao-Sheng Shen, 2020. "Correction to: Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 893-894, October.
    4. Kebabi, Khedidja & Messaci, Fatiha, 2012. "Rate of the almost complete convergence of a kernel regression estimate with twice censored data," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1908-1913.
    5. Pao-Sheng Shen, 2020. "Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 624-637, July.
    6. 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.
    7. Lopez, Olivier & Patilea, Valentin & Van Keilegom, Ingrid, 2013. "Single index regression models in the presence of censoring depending on the covariates," LIDAM Reprints ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Messaci, Fatiha, 2010. "Local averaging estimates of the regression function with twice censored data," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1508-1511, October.
    9. Aouicha, Lamia & Messaci, Fatiha, 2019. "Kernel estimation of the conditional density under a censorship model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 173-180.
    10. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
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