论文标题
具有传播噪声的递归最大线性模型
Recursive max-linear models with propagating noise
论文作者
论文摘要
递归最大线性向量模型通过结构方程模型之间的节点变量之间的因果关系依赖性，在有向的无环图（DAG）和一些外源创新中以其亲本节点的最大线性函数表达每个节点变量。对于这样的模型，存在一个独特的最小值，以其边缘权重矩阵的kleene星矩阵表示，该矩阵标识了该模型，并且可以估算。对于更现实的统计建模，我们引入了一些随机的观察噪声。对这种新的嘈杂模型的概率分析表明，代表非噪声模型分布的独特最小值DAG保持不变且可识别。此外，模型参数在其左限制的最小比率估计器的分布完全取决于噪声变量的分布，直至正常数。在噪声变量的规则变化条件下，我们证明估计的kleene star矩阵在正确的中心和缩放后会收敛到独立的Weibull条目矩阵。
Recursive max-linear vectors model causal dependence between node variables by a structural equation model, expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph (DAG) and some exogenous innovation. For such a model, there exists a unique minimum DAG, represented by the Kleene star matrix of its edge weight matrix, which identifies the model and can be estimated. For a more realistic statistical modeling we introduce some random observational noise. A probabilistic analysis of this new noisy model reveals that the unique minimum DAG representing the distribution of the non-noisy model remains unchanged and identifiable. Moreover, the distribution of the minimum ratio estimators of the model parameters at their left limits are completely determined by the distribution of the noise variables up to a positive constant. Under a regular variation condition on the noise variables we prove that the estimated Kleene star matrix converges to a matrix of independent Weibull entries after proper centering and scaling.
