Related papers: Decompositions of Dependence for High-Dimensional …
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gr\"obner bases. Each variety encodes a collection of matroids, whose flats…
In this paper, we characterize the extremal dependence of $d$ asymptotically dependent variables by a class of random vectors on the $(d-1)$-dimensional hyperplane perpendicular to the diagonal vector $\mathbf1=(1,\ldots,1)$. This…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
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…
We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…
Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
The tail-dependence compatibility problem is introduced. It raises the question whether a given $d\times d$-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a $d$-dimensional random vector.…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
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…
We consider the problem of supervised dimension reduction with a particular focus on extreme values of the target $Y\in\mathbb{R}$ to be explained by a covariate vector $X \in \mathbb{R}^p$. The general purpose is to define and estimate a…
This work is concerned with the limiting spectral distribution of rank-based dependency measures in high dimensions. We provide distribution-free results for multivariate empirical versions of Kendall's $\tau$ and Spearman's $\rho$ in a…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…
Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…