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 -