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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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