Consistent hazard regression estimation by sieved maximum likelihood estimators

We consider maximum. likelihood estimators in general sieve function classes for the estimation of the conditional log-hazard function of a survival time in a censored data model. We prove consistency of these types of estimators under the assumption that the conditional log-hazard function is continuous, by using results from empirical process theory. As special examples we consider feedforward neural network estimators and radial basis function network estimators.