Recursive max-linear vectors provide models for the causal dependence between large values of observed random variables as they are supported on directed acyclic graphs (DAGs). But the standard assumption that all nodes of such a DAG are observed is often unrealistic. We provide necessary and sufficient conditions that allow for a partially observed vector from a regularly varying model to be represented as a recursive max-linear (sub-)model. Our method relies on regular variation and the minimal representation of a recursive max-linear vector. Here the max-weighted paths of a DAG play an essential role. Results are based on a scaling technique and causal dependence relations between pairs of nodes. In certain cases our method can also detect the presence of hidden confounders. Under a two-step thresholding procedure, we show consistency and asymptotic normality of the estimators. Finally, we study our method by simulation, and apply it to nutrition intake data.

翻译：递归最大线性向量为观测随机变量大值之间的因果依赖关系提供了模型，这些变量以有向无环图（DAG）为基础。但是，标准假设该DAG的所有节点均被观测往往不现实。我们给出了必要且充分的条件，使得来自正则变化模型的偏观测向量能被表示为递归最大线性（子）模型。我们的方法依赖于正则变化和递归最大线性向量的最小表示。在此，DAG的最大加权路径发挥了关键作用。结果基于缩放技术和节点对之间的因果依赖关系。在某些情况下，我们的方法还能检测隐藏混淆因子的存在。在两步阈值处理流程下，我们证明了估计量的一致性和渐近正态性。最后，通过模拟研究并应用于营养摄入数据，我们对方法进行了验证。