Heavy-tailed max-linear structural equation models in networks with hidden nodes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911045954568192 |
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| author | Krali, Mario Davison, Anthony C. Klüppelberg, Claudia |
| author_facet | Krali, Mario Davison, Anthony C. Klüppelberg, Claudia |
| contents | Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be unrealistic. We give necessary and sufficient conditions for a partially observed recursive max-linear vector to be representable as a recursive max-linear (sub-)model and provide a graphical algorithm to construct the latter. Our conditions concern the max-weighted paths of a directed acyclic graph and its minimal representation, which play a key role for such models. In the framework of regular variation we translate these conditions into checkable criteria and establish a connection between max-weighted paths and the extremal dependence measure of transformed variables for pairs of nodes. We propose a statistical algorithm to detect bivariate regularly varying recursive max-linear models among the node variables of a directed acyclic graph and show consistency and asymptotic normality of the estimators of the extremal dependence measure under a thresholding procedure. Simulations show that our algorithm performs satisfactorily. We apply it to nutrition intake data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15356 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Heavy-tailed max-linear structural equation models in networks with hidden nodes Krali, Mario Davison, Anthony C. Klüppelberg, Claudia Statistics Theory Methodology 60G70, 62D20, 62G32, 62H22 (Primary) Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be unrealistic. We give necessary and sufficient conditions for a partially observed recursive max-linear vector to be representable as a recursive max-linear (sub-)model and provide a graphical algorithm to construct the latter. Our conditions concern the max-weighted paths of a directed acyclic graph and its minimal representation, which play a key role for such models. In the framework of regular variation we translate these conditions into checkable criteria and establish a connection between max-weighted paths and the extremal dependence measure of transformed variables for pairs of nodes. We propose a statistical algorithm to detect bivariate regularly varying recursive max-linear models among the node variables of a directed acyclic graph and show consistency and asymptotic normality of the estimators of the extremal dependence measure under a thresholding procedure. Simulations show that our algorithm performs satisfactorily. We apply it to nutrition intake data. |
| title | Heavy-tailed max-linear structural equation models in networks with hidden nodes |
| topic | Statistics Theory Methodology 60G70, 62D20, 62G32, 62H22 (Primary) |
| url | https://arxiv.org/abs/2306.15356 |