Using recursive max-linear models (RMLM) one can model dependence between node variables by expressing each node variable as a max-linear function of its parental nodes and some other exogenous noise variable. Motivated by extreme value theory, our focus lies in RMLMs when the noise variables are regularly varying random variables, and the underlying causal structure is a directed acyclic graph (DAG). We propose a scaling technique and use scaling parameters in order to determine a causality re-ordering of the node variables that makes the underlying DAG well-ordered. We show how one can compute all dependence parameters by using scalings. Furthermore, we prove the asymptotic normality of the scalings and dependence parameters when using an empirical estimate for the angular measure. A simulation study shows that the causality re-ordering and estimation procedures perform nicely also in high dimensions.     «

Using recursive max-linear models (RMLM) one can model dependence between node variables by expressing each node variable as a max-linear function of its parental nodes and some other exogenous noise variable. Motivated by extreme value theory, our focus lies in RMLMs when the noise variables are regularly varying random variables, and the underlying causal structure is a directed acyclic graph (DAG). We propose a scaling technique and use scaling parameters in order to determine a causality re-...     »