arXiv subjects

Mario Krali

Publications and source records attributed to Mario Krali.

4 recordsLinked to original sources

arXiv2025

Causal analysis of extreme risk in a network of industry portfolios

We provide a comprehensive review of causal dependence through a max-linear structural equation model. Such models express each node variable as a max-linear function of its parental node variables in a directed acyclic graph and some exogenous innovation. We reformulate results on structure learning and estimation, which we apply to a network of financial data. A new method, based on hard-thresholding and on the Hamming distance, estimates a sparse DAG for extreme risk~propagation.

q-fin.RM↗

arXiv2025

Causal discovery in heavy-tailed linear structural equation models via scalings

Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This paper concerns the linear structural equation model with regularly varying noise variables. We focus on extreme observations generated from such a model and propose a causal discovery method based on the scaling parameters of its extremal angular measure. We implement the method as an algorithm, establish its consistency and evaluate it by simulation and by application to river discharge datasets. Comparison with the only alternative extremal method for such model reveals its competitive performance.

stat.ME↗

arXiv2023

Heavy-tailed max-linear structural equation models in networks with hidden nodes

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.

math.ST↗

arXiv2019

Estimating an Extreme Bayesian Network via Scalings

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.

stat.ME↗