Related papers: Operator Tail Dependence of Copulas
The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…
The omnipotence of copulas when modeling dependence given marg\-inal distributions in a multivariate stochastic situation is assured by the Sklar's theorem. Montes et al.\ (2015) suggest the notion of what they call an \emph{imprecise…
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
We consider a fixed-point equation for a non-negative integer-valued random variable, that appears in branching processes with state-independent immigration. A similar equation appears in the analysis of a single-server queue with a…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
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,…
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
We introduce so-called "single-index copulae". They are semi-parametric conditional copulae whose parameter is an unknown "link" function of a univariate index only. We provide estimates of this link function and of the finite dimensional…
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…
In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
A scan statistic is examined for the purpose of testing the existence of a global peak in a random process with dependent variables of any distribution. The scan statistic tail probability is obtained based on the covariance of the moving…
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…