Afrika Statistika

On the strong convergence of the hazard rate and its maximum risk point estimators in presence of censorship and functional explanatory covariate

Komi Agbokou and Kossi Essona Gneyou

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Abstract

In the literature much work has been devoted to the non-parametric estimation of survival analysis functions. In this work, we focus on the nonparametric estimation of the conditional hazard rate and the point of its maximum, in the model of right censored data with presence of functional covariate. We establish the almost uniform complete convergence of these estimators at appropriate rates. This generalizes the almost sure convergence obtained in the literature.

Résumé

Dans la littérature beaucoup de travaux ont été consacrés à l'estimation non-paramétrique des fonctions d'analyse de survie. Dans ce travail, nous nous focalisons sur l'estimation non-paramétrique du taux de hasard conditionnel et du point de son maximum, dans le modèle des données censurées à droite et en présence de covariable fonctionnelle. Nous établissons la convergence uniforme presque complète de ces estimateurs à des vitesses appropriées. Ce qui généralise la convergence presque sûre obtenue dans la littérature.

Article information

Source
Afr. Stat., Volume 12, Number 3 (2017), 1397-1416.

Dates
Received: 18 June 2017
Accepted: 1 August 2017
First available in Project Euclid: 4 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.as/1515035036

Digital Object Identifier
doi:10.16929/as/2017.1296.110

Mathematical Reviews number (MathSciNet)
MR3743305

Zentralblatt MATH identifier
06825112

Subjects
Primary: 62N01: Censored data models 62N02: Estimation 62P10: Applications to biology and medical sciences 62P12: Applications to environmental and related topics

Keywords
nonparametric estimation conditional hazard rate maximum value censored data small ball probabilities functional random variable

Citation

Agbokou, Komi; Gneyou, Kossi Essona. On the strong convergence of the hazard rate and its maximum risk point estimators in presence of censorship and functional explanatory covariate. Afr. Stat. 12 (2017), no. 3, 1397--1416. doi:10.16929/as/2017.1296.110. https://projecteuclid.org/euclid.as/1515035036


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