Asymptotic properties of the MLE in distributional regression under random censoring

The aim of distributional regression is to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution parameters, a common approach for this task is using the maximum likelihood estimator (MLE) for the parameters. In this paper, we establish theoretical results for this estimator in case the response variable is subject to random right censoring. In particular, we provide proofs of almost sure consistency and asymptotic normality of the MLE under censoring. Further, the finite-sample behavior is exemplarily demonstrated in a simulation study.