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

Abstract

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 ontété consacrésà l'estimation nonparamétrique 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 censuréesà droite et en présence de covariable fonctionnelle. Nousétablissons la convergence uniforme presque complète de ces estimateursà des vitesses appropriées. Ce qui généralise la convergence presque sûre obtenue dans la littérature.

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