A strong linear representation for the maximum conditional hazard rate estimator in survival analysis

Quintela-del-Río (2006) considered the estimation of the maximum hazard under dependence conditions and established strong convergence with rate and asymptotic normality of the estimate. The aim of this paper is to generalize this work to the case of right censored data with covariate. Via a consistently Nadaraya–Watson weighted type estimator of the conditional hazard function, we get a non-parametric estimator of its maximum value. We establish strong representation and strong uniform consistency results for our estimators.