Related papers: Tail dependence and smoothness
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…
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…
To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…
We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…
The tail process $\boldsymbol{Y}=(Y_{\boldsymbol{i}})_{\boldsymbol{i}\in\mathbb{Z}^d}$ of a stationary regularly varying random field $\boldsymbol{X}=(X_{\boldsymbol{i}})_{\boldsymbol{i}\in\mathbb{Z}^d}$ represents the asymptotic local…
We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such…
The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal…
We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of…
In this paper, we propose a novel frequency-severity joint trip-level risk index that combines the frequency of abnormal driving patterns with a severity component reflecting how extreme such behavior is relative to a portfolio-level…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
This paper introduces a copula-based model for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. We establish a unified framework for inference by proving the…
The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…