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graphicalExtremes: Statistical methodology for graphical extreme value models.

Source: R/graphicalExtremes-package.R
graphicalExtremes.Rd

An implementation of the statistical methodology paper Engelke and Hitz (2020) for sparse multivariate extreme value models. Includes exact simulation algorithms and statistical inference methods for multivariate Pareto distributions on graphical structures. Also contains implementations of statistical methods from Engelke and Volgushev (2022) , Röttger et al. (2021) , and Hentschel et al. (2022) .

Details

The following global options are used by functions in the package. Their values can be changed using base::options().

"graphicalExtremes.mc.cores"

The (maximal) number of cores to use in parallel tasks. Will always be overwritten by 1 on Windows.

"graphicalExtremes.tol.small"

The "small" tolerance is used in internal computations for values that should mathematically be exactly equal to zero, but deviate due to inherent limitations of numerical computations. This value is used e.g. when checking matrices for symmetry and definiteness. In general, this value is used only as a "permissive" tolerance, in the sense that if a value has to be positive, it is compared to actual zero, but if it has to be zero, its absolute value is compared to this tolerance.

"graphicalExtremes.tol.large"

The "large" tolerance is used for values that converge to zero, but are mathematically not supposed to be equal to zero. This value is used e.g. when converting a precision matrix \(\Theta\) to an adjacency matrix of a graph.

"graphicalExtremes.default.alert

The default alert function to be used in validity checks of Huesler-Reiss parameter matrix transformations. Can be a function that takes an arbitrary number of strings as arguments (e.g. cat(), stop()), FALSE to ignore the alerts, or TRUE/NULL to use the default function warning().

References

Engelke S, Hitz AS (2020). “Graphical models for extremes (with discussion).” J. R. Stat. Soc. Ser. B Stat. Methodol., 82, 871--932.

Engelke S, Volgushev S (2022). “Structure learning for extremal tree models.” J. R. Stat. Soc. Ser. B Stat. Methodol.. doi:10.1111/rssb.12556 , Forthcoming, https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/rssb.12556.

Hentschel M, Engelke S, Segers J (2022). “Statistical Inference for Hüsler-Reiss Graphical Models Through Matrix Completions.” doi:10.48550/ARXIV.2210.14292 , https://arxiv.org/abs/2210.14292.

Röttger F, Engelke S, Zwiernik P (2021). “Total positivity in multivariate extremes.” doi:10.48550/ARXIV.2112.14727 , https://arxiv.org/abs/2112.14727.

See also

Useful links:

Author

Maintainer: Sebastian Engelke sebastian.engelke@unige.ch

Authors:

  • Adrien S. Hitz

  • Nicola Gnecco

  • Manuel Hentschel