Related papers: Asymmetric dependence in hydrological extremes
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…
Tests of independence are an important tool in applications, specifically in connection with the detection of a relationship between variables; they also have initiated many developments in statistical theory. In the present paper we build…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
Modelling multivariate extreme events is essential when extrapolating beyond the range of observed data. Parametric models that are suitable for real-world extremes must be flexible -- particularly in their ability to capture asymmetric…
Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest…
Fully describing the entire data set is essential in multivariate risk assessment, since moderate levels of one variable can influence another, potentially leading it to be extreme. Additionally, modelling both non-extreme and extreme…
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.…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
We present an index of dependence that allows one to measure the joint or mutual dependence of a $d$-dimensional random vector with $d>2$. The index is based on a $d$-dimensional Kendall process. We further propose a standardized version of…
Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…
The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Archimedean copulas generated by Laplace transforms have been extensively studied in the literature, with much of the focus on tail dependence limited only to cases where the Laplace transforms exhibit regular variation with positive tail…
The climate change dispute is about changes over time of environmental characteristics (such as rainfall). Some people say that a possible change is not so much in the mean but rather in the extreme phenomena (that is, the average rainfall…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram.…
The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…
Correlation and spectral analysis represent the standard tools to study interdependence in statistical data. However, for the stochastic processes with heavy-tailed distributions such that the variance diverges, these tools are inadequate.…