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Related papers: Tails of multivariate Archimedean copulas

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We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positive associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of…

Statistics Theory · Mathematics 2017-09-14 Juan-Juan Cai , Eni Musta

This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the…

Probability · Mathematics 2012-05-01 Damiano Brigo , Kyriakos Chourdakis

Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…

Machine Learning · Computer Science 2022-01-03 Michel Besserve , Rémy Sun , Dominik Janzing , Bernhard Schölkopf

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…

Combinatorics · Mathematics 2017-12-12 Lutz Warnke

We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…

Probability · Mathematics 2022-12-29 Shuyang Bai , Yizao Wang

The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…

Methodology · Statistics 2018-02-06 Linda Mhalla , Thomas Opitz , Valérie Chavez-Demoulin

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

Statistics Theory · Mathematics 2019-02-11 Yaonan Jin , Yingkai Li , Yining Wang , Yuan Zhou

Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…

Methodology · Statistics 2026-04-15 Mirco Lescart , Anna Kiriliouk , Philippe Naveau

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…

Methodology · Statistics 2013-10-01 Abhik Ghosh , Aritra Chakravorty

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan \emph{et al.} allows to also account for asymptotic independence. In this paper we introduce…

Statistics Theory · Mathematics 2012-10-30 Helena Ferreira , Marta Ferreira

Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes,…

Machine Learning · Computer Science 2022-05-04 Andrew McDonald , Pang-Ning Tan , Lifeng Luo

Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…

Machine Learning · Statistics 2022-10-07 Gherardo Varando , Federico Carli , Manuele Leonelli

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

Probability · Mathematics 2019-01-21 Harry Joe , Haijun Li

Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (dfs). Dfs are rarely available in…

Probability · Mathematics 2009-12-23 Guus Balkema , Natalia Nolde

In this paper, we construct a bound copula, which can reach both Frechet's lower and upper bounds for perfect positive and negative dependence cases. Since it covers a wide range of dependency and simple for computational purposes, it can…

Probability · Mathematics 2021-02-01 Suman Thapa , Yiqiang Q. Zhao

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…

Statistics Theory · Mathematics 2016-12-22 Mohsen Ben Hassine , Lamine Mili , Kiran Karra

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.…

Probability · Mathematics 2016-06-28 Paul Embrechts , Marius Hofert , Ruodu Wang

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…

Statistics Theory · Mathematics 2012-10-05 John H. J. Einmahl , Andrea Krajina , Johan Segers

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of…

Statistics Theory · Mathematics 2011-09-30 Axel Bücher , Holger Dette , Stanislav Volgushev

The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having…

Probability · Mathematics 2010-11-11 Xiaolin Luo , Pavel V. Shevchenko