Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme value theory, innovations are assumed to have regularly varying distribution tails. We propose a scaling technique in order to determine a causal order of the node variables. All dependence parameters are then estimated from the estimated scalings. Furthermore, we prove asymptotic normality of the estimated scalings and dependence parameters based on asymptotic normality of the empirical spectral measure. Finally, we apply our structure learning and estimation algorithm to financial data and food dietary interview data.

中文翻译：

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通过缩放估计极端贝叶斯网络

递归最大线性向量通过将每个节点变量表示为其父节点在有向无环图中的最大线性函数和一些外生创新来模拟其组件之间的因果依赖性。在极值理论的推动下，假设创新具有规律性变化的分布尾部。我们提出了一种缩放技术，以确定节点变量的因果顺序。然后从估计的缩放比例估计所有相关参数。此外，我们证明了基于经验谱度量的渐近正态性的估计标度和相关参数的渐近正态性。最后，我们将我们的结构学习和估计算法应用于财务数据和食品饮食访谈数据。