Opuscula Math. 42, no. 6 (2022), 805-832
https://doi.org/10.7494/OpMath.2022.42.6.805

 
Opuscula Mathematica

Strong consistency of the local linear relative regression estimator for censored data

Feriel Bouhadjera
Elias Ould Saïd

Abstract. In this paper, we combine the local linear approach to the relative error regression estimation method to build a new estimator of the regression operator when the response variable is subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Numerical studies, firstly on simulated data, then on a real data set concerning the death times of kidney transplant patients, were conducted. These practical studies clearly show the superiority of the new estimator compared to competitive estimators.

Keywords: censored data, local linear approach, relative error, regression function, uniform almost sure convergence.

Mathematics Subject Classification: 62N01, 62N02, 62G08, 62G35, 62P10.

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  • Elias Ould Saïd
  • ORCID iD https://orcid.org/0000-0002-5068-3140
  • Université du Littoral Côte d'Opale, Laboratoire de Mathématiques Pures et Appliquées, IUT de Calais, 19, rue Louis David, Calais, 62228, France
  • Communicated by Mirosław Pawlak.
  • Received: 2021-03-19.
  • Revised: 2022-04-19.
  • Accepted: 2022-08-02.
  • Published online: 2022-11-24.
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Cite this article as:
Feriel Bouhadjera, Elias Ould Saïd, Strong consistency of the local linear relative regression estimator for censored data, Opuscula Math. 42, no. 6 (2022), 805-832, https://doi.org/10.7494/OpMath.2022.42.6.805

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