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On nonparametric estimation of the regression function under random censorship model

Author

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  • Guessoum Zohra

    (Univ. des Sci. et Tech. H. B., Faculté de Mathématiques, El Alia, Algerien)

  • Ould-Said Elias

Abstract

In this paper, we study the behavior of a kernel estimator for the regression function in a random right-censoring model. We establish pointwise and uniform strong consistency over a compact set and give a rate of convergence for the estimate.The asymptotic normality of the estimate is also proved. Simulations are drawn for different cases to illustrate both, convergence and asymptotic normality.

Suggested Citation

  • Guessoum Zohra & Ould-Said Elias, 2009. "On nonparametric estimation of the regression function under random censorship model," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 159-177, April.
    • Handle: RePEc:bpj:strimo:v:26:y:2009:i:3:p:159-177:n:2
    DOI: 10.1524/stnd.2008.0919
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    References listed on IDEAS

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    1. 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.
    2. Györfi, László & Walk, Harro, 1997. "On the strong universal consistency of a recursive regression estimate by Pál Révész," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 177-183, January.
    3. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    4. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 357-378, June.
    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.
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