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

• Published in: Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 42; no. 6; pp. 805 - 832
• Main Authors: Bouhadjera, Feriel, Said, Elias Ould
• Format: Journal Article
• Language: English
• Published: AGH University of Science and Technology 01.01.2022; AGH Univeristy of Science and Technology Press
• Subjects: censored data; local linear approach; Mathematics; regression function; relative error; Statistics; uniform almost sure convergence; local linear approach; censored data; relative error; regression function; uniform almost sure convergence
• ISSN: 1232-9274; 2300-6919
• DOI: 10.7494/OpMath.2022.42.6.805

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.