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

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. Keywords: Nonparametric estimation; conditional hazard rate maximum value; censored data; small ball probabilities; functional random variable