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Document type:
Masterarbeit
Author(s):
Gian Luca Esposito
Title:
Identifiability and Estimation of Recursive Max-Linear Models
Abstract:
A recursive max-linear model is a structural equation model in which the dependence structure between the random variables is represented by a directed acyclic graph. In comparison to usual Gaussian structural equation models sums are replaced by maxima and the Gaussian distribution is replaced by the standard Fréchet-distribution. Hence, well-known estimation methods that uses conditional independence to infer the structure of the underlying unknown DAG cannot be applied anymore. In this thesis, we develop a new Branch & Bound algorithm to estimate the topological order of the nodes of a recursive max-linear model with underlying unknown directed acyclic graph. We extend the recursive max-linear model and introduce multiplicative noise in two different ways, first in a recursive manner and then as Hadamard product in order to test the new algorithm also in situations that come close to real world scenarios. A simulation study shows that the new algorithm performs very well, if we have non-noisy observations as well as if we have noisy observations.
Keywords:
Graphical Models, Recursive Max-Linear Models, Greedy Algorithm, Branch and Bound
Subject:
MAT Mathematik
DDC:
510 Mathematik
Advisor:
Claudia Klüppelberg and Johannes Buck
Year:
2019
Quarter:
2. Quartal
Year / month:
2019-04
Month:
Apr
Language:
en
University:
Technische Universität München
Faculty:
Fakultät für Mathematik
TUM Institution:
Lehrstuhl für Mathematische Statistik
Format:
Text
ingested:
30.04.2019
Status:
abgeschlossen
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