Related papers: Multivariate tail dependence and local stochastic …
A new class of copulas based on order statistics was introduced by Baker (2008). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate…
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows - in contrast to finite partition-of-unity copulas - for tail-dependence as well as for asymmetry. A possibility…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
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,…
We study the tail bound of the emperical covariance of multivariate normal distribution. Following the work of (Gittens & Tropp, 2011), we provide a tail bound with a small constant.
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…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss some aspects of dependence between the components of a…
Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects.…
Stochastic dominance has been studied extensively, particularly in the finance and economics literature. In this paper, we obtain two results. First, necessary conditions for higher-order inverse stochastic dominance are developed. These…
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…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
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…
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…
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…
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.…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…