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.

翻译：分布回归的目标是在给定的条件分布参数族中寻找最优候选分布以建模给定数据集。由于分布族中的每个候选分布可通过相应的分布参数唯一确定，该任务的常用方法是使用参数的极大似然估计量。本文针对响应变量受随机右删失的情形，建立了该估计量的理论结果。特别地，我们证明了删失情况下极大似然估计的几乎必然相合性与渐近正态性。此外，通过模拟研究示例性地展示了其有限样本性质。