2023/06/27 by Mario Krali, Krali, Mario, A. C. Davison +3 · 3 citations
Physics and Astronomy · #60G70 #62D20 #62G32 #62H22 (Primary) #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2306.15356
openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be unrealistic. We give necessary and sufficient conditions for a partially observed recursive max-linear vector to be representable as a recursive max-linear (sub-)model and provide a graphical algorithm to construct the latter. Our conditions concern the max-weighted paths of a directed acyclic graph and its minimal representation, which play a key role for such models. In the framework of regular variation we translate these conditions into checkable criteria and establish a connection between max-weighted paths and the extremal dependence measure of transformed variables for pairs of nodes. We propose a statistical algorithm to detect bivariate regularly varying recursive max-linear models among the node variables of a directed acyclic graph and show consistency and asymptotic normality of the estimators of the extremal dependence measure under a thresholding procedure. Simulations show that our algorithm performs satisfactorily. We apply it to nutrition intake data.