Identifiability and estimation of recursive max‐linear models
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Identifiability and estimation of recursive max‐linear models. / Gissibl, Nadine; Klüppelberg, Claudia; Lauritzen, Steffen.
In: Scandinavian Journal of Statistics, Vol. 48, No. 1, 2021, p. 188-211.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Identifiability and estimation of recursive max‐linear models
AU - Gissibl, Nadine
AU - Klüppelberg, Claudia
AU - Lauritzen, Steffen
PY - 2021
Y1 - 2021
N2 - We address the identifiability and estimation of recursive max‐linear structural equation models represented by an edge‐weighted directed acyclic graph (DAG). Such models are generally unidentifiable and we identify the whole class of DAG s and edge weights corresponding to a given observational distribution. For estimation, standard likelihood theory cannot be applied because the corresponding families of distributions are not dominated. Given the underlying DAG, we present an estimator for the class of edge weights and show that it can be considered a generalized maximum likelihood estimator. In addition, we develop a simple method for identifying the structure of the DAG. With probability tending to one at an exponential rate with the number of observations, this method correctly identifies the class of DAGs and, similarly, exactly identifies the possible edge weights.
AB - We address the identifiability and estimation of recursive max‐linear structural equation models represented by an edge‐weighted directed acyclic graph (DAG). Such models are generally unidentifiable and we identify the whole class of DAG s and edge weights corresponding to a given observational distribution. For estimation, standard likelihood theory cannot be applied because the corresponding families of distributions are not dominated. Given the underlying DAG, we present an estimator for the class of edge weights and show that it can be considered a generalized maximum likelihood estimator. In addition, we develop a simple method for identifying the structure of the DAG. With probability tending to one at an exponential rate with the number of observations, this method correctly identifies the class of DAGs and, similarly, exactly identifies the possible edge weights.
U2 - 10.1111/sjos.12446
DO - 10.1111/sjos.12446
M3 - Journal article
VL - 48
SP - 188
EP - 211
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 1
ER -
ID: 240251371