TY - JOUR

T1 - Tail dependence of recursive max-linear models with regularly varying noise variables

AU - Gissibl, Nadine

AU - Klüppelberg, Claudia

AU - Otto, Moritz

N1 - Publisher Copyright:
© 2018 EcoSta Econometrics and Statistics

PY - 2018/4

Y1 - 2018/4

N2 - Recursive max-linear structural equation models with regularly varying noise variables are considered. Their causal structure is represented by a directed acyclic graph (DAG). The problem of identifying a recursive max-linear model and its associated DAG from its matrix of pairwise tail dependence coefficients is discussed. For example, it is shown that if a causal ordering of the associated DAG is additionally known, then the minimum DAG representing the recursive structural equations can be recovered from the tail dependence matrix. For a relevant subclass of recursive max-linear models, identifiability of the associated minimum DAG from the tail dependence matrix and the initial nodes is shown. Algorithms find the associated minimum DAG for the different situations. Furthermore, given a tail dependence matrix, an algorithm outputs all compatible recursive max-linear models and their associated minimum DAGs.

AB - Recursive max-linear structural equation models with regularly varying noise variables are considered. Their causal structure is represented by a directed acyclic graph (DAG). The problem of identifying a recursive max-linear model and its associated DAG from its matrix of pairwise tail dependence coefficients is discussed. For example, it is shown that if a causal ordering of the associated DAG is additionally known, then the minimum DAG representing the recursive structural equations can be recovered from the tail dependence matrix. For a relevant subclass of recursive max-linear models, identifiability of the associated minimum DAG from the tail dependence matrix and the initial nodes is shown. Algorithms find the associated minimum DAG for the different situations. Furthermore, given a tail dependence matrix, an algorithm outputs all compatible recursive max-linear models and their associated minimum DAGs.

KW - Causal inference

KW - Directed acyclic graph

KW - Extreme value theory

KW - Graphical model

KW - Max-linear model

KW - Max-stable model

KW - Regular variation

KW - Structural equation model

KW - Tail dependence coefficient

UR - http://www.scopus.com/inward/record.url?scp=85045844053&partnerID=8YFLogxK

U2 - 10.1016/j.ecosta.2018.02.003

DO - 10.1016/j.ecosta.2018.02.003

M3 - Article

AN - SCOPUS:85045844053

SN - 2452-3062

VL - 6

SP - 149

EP - 167

JO - Econometrics and Statistics

JF - Econometrics and Statistics

ER -