Distributional regression aims 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 to use 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. The empirical behavior is illustrated by a simulation study and a real data example.

翻译：分布回归旨在从给定的条件分布参数族中，寻找最优候选模型来拟合特定数据集。由于分布族中的每个候选模型可通过对应的分布参数唯一识别，常用方法之一是采用参数的最大似然估计（MLE）。本文针对响应变量存在随机右删失的情况，建立了该估计量的理论结果。具体而言，我们证明了删失条件下MLE的几乎一致相合性和渐近正态性。通过模拟研究和实际数据案例，验证了其经验表现。