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Jennifer Wadsworth

Publications and source records attributed to Jennifer Wadsworth.

9 recordsLinked to original sources
arXiv2026

Geometric extremal graphical models and coefficients of extremal dependence on block graphs

We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating to the propagation of various extremal dependence coefficients along the graph. A particular focus is placed on coefficients that link to the framework of conditional extreme value theory, which are especially interesting when variables do not all attain their most extreme values simultaneously. We also consider results related to the case when variables do exhibit joint extreme behaviour. Through the recent translation of the geometric approach for multivariate extremes to a statistical modelling framework, geometric extremal graphical models, and results relating to them, pave the way for an approach to modelling of high dimensional extremes with complex extremal dependence structures.

math.ST↗
arXiv2025

Geometric criteria for identifying extremal dependence and flexible modeling via additive mixtures

The framework of geometric extremes is based on the convergence of scaled sample clouds onto a limit set, characterized by a gauge function, with the shape of the limit set determining extremal dependence structures. While it is known that a blunt limit set implies asymptotic independence, the absence of bluntness can be linked to both asymptotic dependence and independence. Focusing on the bivariate case, under a truncated gamma modeling assumption with bounded angular density, we show that a ``pointy'' limit set implies asymptotic dependence, thus offering practical geometric criteria for identifying extremal dependence classes. Suitable models for the gauge function offer the ability to capture asymptotically independent or dependent data structures, without requiring prior knowledge of the true extremal dependence structure. The geometric approach thus offers a simple alternative to various parametric copula models that have been developed for this purpose in recent years. We consider two types of additively mixed gauge functions that provide a smooth interpolation between asymptotic dependence and asymptotic independence. We derive their explicit forms, explore their properties, and establish connections to the developed geometric criteria. Through a simulation study, we evaluate the effectiveness of the geometric approach with additively mixed gauge functions, comparing its performance to existing methodologies that account for both asymptotic dependence and asymptotic independence. The methodology is computationally efficient and yields reliable performance across various extremal dependence scenarios.

stat.ME↗
arXiv2024

Piecewise-linear modeling of multivariate geometric extremes

A recent development in extreme value modeling uses the geometry of the dataset to perform inference on the multivariate tail. A key quantity in this inference is the gauge function, whose values define this geometry. Methodology proposed to date for capturing the gauge function either lacks flexibility due to parametric specifications, or relies on complex neural network specifications in dimensions greater than three. We propose a semiparametric gauge function that is piecewise-linear, making it simple to interpret and provides a good approximation for the true underlying gauge function. This linearity also makes optimization tasks computationally inexpensive. The piecewise-linear gauge function can be used to define both a radial and an angular model, allowing for the joint fitting of extremal pseudo-polar coordinates, a key aspect of this geometric framework. We further expand the toolkit for geometric extremal modeling through the estimation of high radial quantiles at given angular values via kernel density estimation. We apply the new methodology to air pollution data, which exhibits a complex extremal dependence structure.

stat.ME↗
arXiv2024

Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes

Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the `state-of-the-art' in many applied fields. However, while the asymptotic theory supporting the use of max-stable processes is mathematically rigorous and comprehensive, we think that it has also been overused, if not misused, in environmental applications, to the detriment of more purposeful and meticulously validated models. In this paper, we review the main limitations of max-stable process models, and strongly argue against their systematic use in environmental studies. Alternative solutions based on more flexible frameworks using the exceedances of variables above appropriately chosen high thresholds are discussed, and an outlook on future research is given, highlighting recommendations moving forward and the opportunities offered by hybridizing machine learning with extreme-value statistics.

stat.ME↗
arXiv2023

Statistical inference for multivariate extremes via a geometric approach

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically-motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches, and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit.

stat.ME↗
arXiv2019

Extremal dependence of random scale constructions

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of vectors with a random scale construction $(X_1,X_2)=R(W_1,W_2)$, with non-degenerate $R>0$ independent of $(W_1,W_2)$. Focusing on the presence and strength of asymptotic tail dependence, as expressed through commonly-used summary parameters, broad factors that affect the results are: the heaviness of the tails of $R$ and $(W_1,W_2)$, the shape of the support of $(W_1,W_2)$, and dependence between $(W_1,W_2)$. When $R$ is distinctly lighter tailed than $(W_1,W_2)$, the extremal dependence of $(X_1,X_2)$ is typically the same as that of $(W_1,W_2)$, whereas similar or heavier tails for $R$ compared to $(W_1,W_2)$ typically result in increased extremal dependence. Similar tail heavinesses represent the most interesting and technical cases, and we find both asymptotic independence and dependence of $(X_1,X_2)$ possible in such cases when $(W_1,W_2)$ exhibit asymptotic independence. The bivariate case often directly extends to higher-dimensional vectors and spatial processes, where the dependence is mainly analyzed in terms of summaries of bivariate sub-vectors. The results unify and extend many existing examples, and we use them to propose new models that encompass both dependence classes.

math.PR↗
arXiv2017

Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets

Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, or other suitable covariate. Working within a framework of asymptotic dependence, we introduce a regression model for the angular density of a bivariate extreme value distribution that allows us to assess how extremal dependence evolves over a covariate. We apply the proposed model to assess the dynamics governing extremal dependence of some leading European stock markets over the last three decades, and find evidence of an increase in extremal dependence over recent years.

q-fin.ST↗
arXiv2015

Modelling across extremal dependence classes

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for, but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on sub-domains, or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios, and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model, and show that it performs well in a range of settings.

stat.ME↗