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Nonparametric robust regression estimation for censored data

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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.

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Notes

  1. Note that the strict monotonicity is a sufficient but not necessary assumption as can be seen in the \(\alpha \)-quantile and Huber cases.

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Acknowledgments

The authors are grateful to an anonymous referee whose careful and thorough reading gave them the opportunity to improve the quality of the paper.

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Authors and Affiliations

  1. Lab. Biomathématiques, Fac. de Pharmacie, Univ. de Lille 2., 3, rue du Pr. Laguesse, 59006, Lille, France

    Mohamed Lemdani

  2. Univ. Lille Nord de France, 59000, Lille, France

    Elias Ould Saïd

  3. Univ. du Littoral Côte d’Opale, LMPA, 62228, Calais, France

    Elias Ould Saïd

Authors
  1. Mohamed Lemdani
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  2. Elias Ould Saïd
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Correspondence to Mohamed Lemdani.

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Lemdani, M., Ould Saïd, E. Nonparametric robust regression estimation for censored data. Stat Papers 58, 505–525 (2017). https://doi.org/10.1007/s00362-015-0709-8

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  • DOI: https://doi.org/10.1007/s00362-015-0709-8

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