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In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…

Statistics Theory · Mathematics 2022-08-17 Jordan Richards , Jonathan A. Tawn

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…

Methodology · Statistics 2019-12-06 Shrijita Bhattacharya , Jan Beirlant

We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…

Probability · Mathematics 2025-06-25 Bojan Basrak , Ilya Molchanov , Hrvoje Planinić

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…

Methodology · Statistics 2021-01-06 Sebastian Engelke , Jevgenijs Ivanovs

A family of Virtual Element schemes based on the Hellinger-Reissner variational principle is presented. A convergence and stability analysis is rigorously developed. Numerical tests confirming the theoretical predictions are performed.

Numerical Analysis · Mathematics 2018-08-01 Edoardo Artioli , Stefano de Miranda , Carlo Lovadina , Luca Patruno

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…

Methodology · Statistics 2014-10-27 Axel Bücher , Ivan Kojadinovic

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

Statistics Theory · Mathematics 2019-02-20 Thomas Lugrin , Anthony C. Davison , Jonathan A. Tawn

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…

Statistics Theory · Mathematics 2022-11-28 Natalia Markovich

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Machine Learning · Statistics 2024-10-29 Hanwen Huang , Peng Zeng

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…

Methodology · Statistics 2021-02-16 Pavel Krupskii , Marc G. Genton

In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains…

Statistics Theory · Mathematics 2025-09-26 Bikramjit Das , Vicky Fasen-Hartmann

We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. This framework enables…

Methodology · Statistics 2017-10-17 Daniel Cooley , Emeric Thibaud , Federico Castillo , Michael F. Wehner

Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and…

Machine Learning · Statistics 2016-03-15 Nicolas Goix , Anne Sabourin , Stéphan Clémençon

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…

Statistics Theory · Mathematics 2023-02-28 Steven De Keyser , Irène Gijbels

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

Applications · Statistics 2014-12-31 Alexis Bienvenüe , Christian Y. Robert

This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample…

Statistics Theory · Mathematics 2021-09-06 Nazar Buzun , Nikolay Shvetsov , Dmitry V. Dylov

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…

Methodology · Statistics 2026-01-13 Roberto Fontana , Elisa Perrone , Fabio Rapallo

Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common…

Combinatorics · Mathematics 2025-01-28 Yun Cheng , Yixue Liu , Tomasz Tkocz , Albert Xu

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…

Statistics Theory · Mathematics 2007-06-13 John H. J. Einmahl , Tao Lin