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:统计审查制度的范围扩大到可以将随机措施用于实现数据点的情况,从而形成一种将专家信息纳入通常的参数估计程序的新方法,为由此得出的估计者提供无药可治理论,并更详细地研究一些具有实际相关性的特殊案例,虽然拟议的框架从数学上概括了随机审查和粗略分析,并借用了M估测理论的技术,但它提供了一种新颖和透明的方法,在有专家信息的情况下,这种方法具有重大的实际适用性,具体地对高规格的MTPL数据集采用尾线参数估计,而现有专家信息有限,说明了这种方法的潜力。