Related papers: Multivariate Tail Estimation: Conditioning on an e…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
The aim of this paper is to study the asymptotic behavior of a particular multivariate risk measure, the Covariate-Conditional-Tail-Expectation (CCTE), based on a multivariate statistical depth function. Depth functions have become…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…
Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome.…
In this paper we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk…
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…
In this paper, we consider the problem of the estimation of a Weibull tail-coefficient. In particular, we propose a regression model, from which we derive a bias-reduced estimator. This estimator is based on a least-squares approach. The…
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…