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

Abstract

a b s t r a c t 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.

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

“…We applied the result to the nonparametric estimation of the high-risk point dependent on the covariate. This convergence can also be uniform in both time and space (covariate) by restricting the covariate to vary in a compact subspace of F (see in Gneyou (2013Gneyou ( , 2014). We undertook a numerical study.…”

“…(1.4) Gneyou (2013) and Gneyou (2014) established almost sure representations and the asymptotic normality of a maximum risk estimator in the right-censored data model. This estimator is obtained via the conditional cumulative hazard rate by convolution with a kernel.…”

Counterfactual Inference in Duration Models with Random Censoring

“…Assumptions I1 and I2 are commonly imposed in survival analysis, for example Lancaster (1992) and Kalbfleisch and Prentice (2002) for Assumption I1 and Dabrowska (1989), Iglesias-Pérez and González-Manteiga (1999), and Gneyou (2014) for Assumption I2. Assumption I1 ensures that the random censoring is non-informative; that is, C does not provide any information about T , and vice versa.…”