The statistical censoring setup is extended to the situation when random measures can be assigned to the realization of datapoints, leading to a new way of incorporating expert information into the usual parametric estimation procedures. The asymptotic theory is provided for the resulting estimators, and some special cases of practical relevance are studied in more detail. Although the proposed framework mathematically generalizes censoring and coarsening at random, and borrows techniques from M-estimation theory, it provides a novel and transparent methodology which enjoys significant practical applicability in situations where expert information is present. The potential of the approach is illustrated by a concrete actuarial application of tail parameter estimation for a heavy-tailed MTPL dataset with limited available expert information.

翻译：统计删失框架被扩展至可对数据点实现分配随机测度的情形，从而为将专家信息纳入常规参数估计过程提供了新方法。本文给出了所得估计量的渐近理论，并详细研究了若干具有实际意义的特例。尽管所提出的框架在数学上概括了随机删失与粗化机制，并借鉴了M估计理论的技术手段，但它提供了一种新颖且透明的方法论，在存在专家信息的场景中具有显著的实际应用价值。通过一个具体的精算应用——针对有限可用专家信息下的重尾MTPL数据集进行尾部参数估计——展示了该方法的潜力。