Current dependence models for spatial extremes are based upon max-stable processes. Within this class, there few inferentially viable available, and we propose one further model. More problematic the restrictive assumptions that must be made when using processes to model extremes: it assumed structure of observed is compatible with a limiting holds all events more extreme than those have already occurred. This problem has long been acknowledged in context finite-dimensional multivariate...

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that property known asymptotic independence. However, does not automatically imply independence, and whether the process is truly asymptotically (in)dependent usually far from clear. The distinction key it have large impact upon extrapolation, is, estimated...

Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class models extreme values spatial processes. Until recently, inference max-stable has been restricted to use pairwise composite likelihoods, due intractability higher-dimensional distributions. In this work we consider random fields that are in domain attraction a widely used namely those constructed via manipulation...

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or most cases, both these. We present an approach extreme value theory based on conditional multivariate model, whereby limit is formed through conditioning upon at a particular site being extreme. The ensuing methodology allows flexible class structures, as well be fitted dimensions. To overcome issues single site, we...

Abstract Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models perhaps peaked with statisticians, they are still perceived and considered as “state art” in many applied fields. However, while asymptotic theory supporting use processes is mathematically rigorous comprehensive, we think that it also been overused, if not misused, environmental applications, to detriment more purposeful meticulously...

Summary Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class models. In bivariate the variables are either asymptotically dependent or independent. Most available statistical models suit one other these cases, but not both, resulting a stage inference that is unaccounted for substantially impact subsequent extrapolation. Existing modelling solutions to this problem applicable only on subdomains appeal multiple limit theories....

When assessing the impact of extreme events, it is often not just a single component, but combined behavior several components which important. Statistical modeling using multivariate generalized Pareto (GP) distributions constitutes analogue univariate peaks over thresholds modeling, widely used in finance and engineering. We develop general methods for construction GP use them to create variety new statistical models. A censored likelihood procedure proposed make inference on these models,...

Abstract 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, approach itself not fully exploited statistical inference. We outline a method parametric estimation set shape, which includes useful non-/semi-parametric estimate as pre-processing step. More...

Summary For extreme value modelling based on threshold techniques, a well-documented issue is the sensitivity of inference from model to choice threshold. The above which we assume non-homogeneous Poisson process, or equivalently generalized Pareto representation, be reasonable approximation distribution traditionally selected before analysis and subsequently treated as fixed known. In doing so, analyst cannot account for subjective judgement that has already taken place formal begins. We...

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 finance, insurance meteorology, it is crucial to understand which two regimes occurs. Motivated by their ubiquity and flexibility, we consider extremal properties vectors with scale construction $(X_1,X_2)=R(W_1,W_2)$, non-degenerate $R>0$ independent $(W_1,W_2)$. Focusing on presence strength tail...

Abstract The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial spatio-temporal settings. After standardizing the marginal distributions applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models process conditioned on threshold exceedances at a fixed reference location time. In this work, we adapt existing allow handling large...

In many practical applications, evaluating the joint impact of combinations environmental variables is important for risk management and structural design analysis. When such are considered simultaneously, non-stationarity can exist within both marginal distributions dependence structure, resulting in complex data structures. context extremes, few methods have been proposed modelling trends extremal dependence, even though capturing this feature quantifying impact. Moreover, most techniques...

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components a random vector, standardized to identical margins, grow at same rate. In this paper, we consider effect allowing different rates, and characterize link between these marginal growth rates tail probability decay Our approach leads whole class univariate regular variation conditions, in place single but conditions that underpin current theories. These are indexed by...

Multivariate peaks over thresholds modelling based on generalized Pareto distributions has up to now only been used in few and mostly two-dimensional situations. This paper contributes theoretical understanding, models which can respect physical constraints, inference tools, simulation methods support routine use, with an aim at higher dimensions. We derive a general point process model for extreme episodes data, show how conditioning the distribution of threshold exceedance gives four basic...

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

Summary In multivariate extreme value analysis, the nature of extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets can take their largest values simultaneously while others are smaller order. Our approach to this problem exploits hidden regular variation properties on a collection nonstandard cones, and provides new set indices that reveal aspects structure not available through existing...

Abstract The study of multivariate extremes is dominated by regular variation, although it well known that this approach does not provide adequate distinction between random vectors whose components are always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden variation conditional extreme value model. These varying depictions extremal arise through consideration different parts domain, particularly...

To model the tail of a distribution, one has to define threshold above or below which an extreme value produces suitable fit. Parameter stability plots, whereby plots maximum likelihood estimates supposedly threshold-independent parameters against threshold, form main tools for selection by practitioners, principally due their simplicity. However, repeated criticism these is lack interpretability, with pointwise confidence intervals being strongly dependent across range thresholds. In this...

Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration spatio-temporal extensions. This neglects an important feature events: their evolution over time. Many existing models for case are limited by number locations they can handle; this impedes extension to space-time settings, where higher dimensions required. Moreover, that do exist restrictive in terms range extremal dependence types capture....

Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, |$d$|-dimensional likelihood usually precluded due to large number terms in likelihood. However, some studies have noted bias performing that incorporates such event particularly dependence weak. We elucidate phenomenon, showing unbiased moderate dimensions, dimension |$d$| should be a...

Abstract Modelling the extremal dependence of bivariate variables is important in a wide variety practical applications, including environmental planning, catastrophe modelling and hydrology. The majority these approaches are based on framework regular variation, range literature available for estimating structure this setting. However, such procedures only applicable to exhibiting asymptotic dependence, even though independence often observed practice. In paper, we consider so-called...

We investigate the effect that choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses variables from a single process on scales which are linked by nonlinear transformation may lead to discrepant conclusions concerning tail behavior process. propose use Box--Cox power incorporated as part procedure account parametrically for uncertainty surrounding extrapolation. This additional feature increasing rate convergence distribution tails an...

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these is computationally prohibitive, even moderate dimensions, due to necessity of repeatedly evaluating multivariate Gaussian distribution function. In this work, we attempt achieve truly high-dimensional extremes processes, while retaining desirable flexibility structure, by modifying an established class based on scale mixtures processes. We show...