Related papers: Tail processes for stable-regenerative multiple-st…
Statistical modeling of high dimensional extremes remains challenging and has generally been limited to moderate dimensions. Understanding structural relationships among variables at their extreme levels is crucial both for constructing…
The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…
The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…
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…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by…
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We investigate long and short memory in $\alpha$-stable moving averages and max-stable processes with $\alpha$-Fr\'echet marginal distributions. As these processes are heavy-tailed, we rely on the notion of long range dependence suggested…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our…
A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence…
Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk…