Related papers: On the Copula for multivariate Extreme Value distr…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
Driven by the interest on how uniformity of marginal distributions propa\-gates to properties of regression functions, in this contribution we tackle the following questions: Given a $(d-1)$-dimensional random vector $\textbf{X}$ and a…
We consider the extreme value statistics of $N$ independent and identically distributed random variables, which is a classic problem in probability theory. When $N\to\infty$, fluctuations around the maximum of the variables are described by…
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…
Motivated by recently investigated results on dependence measures and robust risk models, this paper provides an overview of dependence properties of many well-known bivariate copula families, where the focus is on the Schur order for…
The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
Estimating mutual information (MI) is a fundamental task in data science and machine learning. Existing estimators mainly rely on either highly flexible models (e.g., neural networks), which require large amounts of data, or overly…
Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have…
One of the main topics of extreme value analysis is to estimate the extreme value index, an important parameter that controls the tail behavior of the distribution. In many cases, estimating the extreme value index of the target variable…
Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with…
Methods are developed for checking and completing systems of bivariate and multivariate Kendall's tau concordance measures in applications where only partial information about dependencies between variables is available. The concept of a…
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…
In extreme value analysis, the extreme value index plays a vital role as it determines the tail heaviness of the underlying distribution and is the primary parameter required for the estimation of other extreme events. In this paper, we…
We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is…
In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…
The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…
In this work, we propose extropy measures based on density copula, distributional copula, and survival copula, and explore their properties. We study the effect of monotone transformations for the proposed measures and obtain bounds. We…
Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is…
Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…