Abstract:
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In this study, we propose a novel extremal dependence measure, called the partial tail correlation coefficient (PTCC), which is an analogy of the partial correlation coefficient in the non-extreme setting. The construction of this coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show that this coefficient is helpful to identify "partial tail uncorrelatedness” relationships between variables. Unlike other recently introduced asymptotic independence frameworks for extremes, our proposed coefficient relies on minimal modeling assumptions and can thus be used generally in exploratory analyses to learn extremal graphical models. Moreover, thanks to its links to traditional graphical models, classical inference methods for high-dimensional data, such as the graphical LASSO with Laplacian spectral constraints, can here also be exploited to efficiently learn extremal networks via the PTCC. We apply these new tools to assess risks in two different network applications, namely extreme river discharges in the upper Danube basin, and historical global currency exchange rate data.
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