Extreme Dependence Models

@article{Beranger2015ExtremeDM,
  title={Extreme Dependence Models},
  author={Boris Beranger and Simone A. Padoan},
  journal={arXiv: Methodology},
  year={2015},
  pages={325-352}
}
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these events is of fundamental importance. For this purpose, probabilistic models and statistical methods are in high demand. There are several approaches to modelling multivariate extremes as described in Falk et al. (2011), linked to some extent. We describe an… 

Figures and Tables from this paper

A semi‐parametric stochastic generator for bivariate extreme events
The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate
Modeling Concurrent Hydroclimatic Extremes With Parametric Multivariate Extreme Value Models
Estimating the dependence structure of concurrent extremes is a fundamental issue for accurate assessment of their occurrence probabilities. Identifying the extremal dependence behavior is also
High-dimensional inference using the extremal skew-t process
TLDR
This article establishes the theoretical formulae for simulations of and inference for the extremal skew- t process, and incorporates the Stephenson-Tawn concept into the composite likelihood framework, giving greater statistical and computational efficiency for higher-order composite likelihoods.
Exploratory data analysis for moderate extreme values using non-parametric kernel methods
In many settings it is critical to accurately model the extreme tail behaviour of a random process. Non-parametric density estimation methods are commonly implemented as exploratory data analysis
Estimation and uncertainty quantification for extreme quantile regions
TLDR
Univariate and bivariate schemes for estimating extreme quantile regions under the Bayesian paradigm that outperforms existing approaches and provides natural measures of quantile region estimate uncertainty are developed.
Bayesian Inference for the Extremal Dependence
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the
Joint inference on extreme expectiles for multivariate heavy-tailed distributions
The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant,
Strong Consistency of Nonparametric Bayesian Inferential Methods for Multivariate Max-Stable Distributions
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a
Tail density estimation for exploratory data analysis using kernel methods
TLDR
A transformation kernel density estimator is developed which is able to handle heavy tailed and bounded data, and is robust to threshold choice, and derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region.
Models for Extremal Dependence Derived from Skew‐symmetric Families
Skew‐symmetric families of distributions such as the skew‐normal and skew‐t represent supersets of the normal and t distributions, and they exhibit richer classes of extremal behaviour. By defining a
...
1
2
...

References

SHOWING 1-10 OF 55 REFERENCES
Extreme dependence models based on event magnitude
Modelling multivariate extreme value distributions
SUMMARY Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the depen- dence between the
A conditional approach for multivariate extreme values
Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d-dimensional random variable. Existing approaches
Modelling Extreme Multivariate Events
SUMMARY The classical treatment of multivariate extreme values is through componentwise ordering, though in practice most interest is in actual extreme events. Here the point process of observations
An Introduction to Statistical Modeling of Extreme Values
  • E. Smith
  • Computer Science
    Technometrics
  • 2002
TLDR
Stuart Coles’s book on the modeling of extreme values provides an introductory text on the topic, a modeling-oriented text with an emphasis on different types of data and analytical approaches, meant for individuals with moderate statistical background.
Statistics for near independence in multivariate extreme values
We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We
A conditional approach for multivariate extreme values (with discussion)
Summary.  Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d‐dimensional random variable. Existing
Dependence modelling for spatial extremes
Current dependence models for spatial extremes are based upon max-stable processes. Within this class, there are few inferentially viable models available, and we propose one further model. More
MAX-STABLE PROCESSES AND SPATIAL EXTREMES
Max-stable processes arise from an infinite-dimensional generalisation of extreme value theory. They form a natural class of processes when sample maxima are observed at each site of a spatial
Bayesian model averaging for multivariate extremes
The main framework of multivariate extreme value theory is well-known in terms of probability, but inference and model choice remain an active research field. Theoretically, an angular measure on the
...
1
2
3
4
5
...