Related papers: Extreme value analysis for mixture models with hea…
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…
We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning Random Matrix Theory and the generalisation of the Tracy-Widom…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…
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…
We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
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…
Extreme-value copulas arise as the limiting dependence structure of component-wise maxima. Defined in terms of a functional parameter, they are one of the most widespread copula families due to their flexibility and ability to capture…
The estimation of asset return distributions is crucial for determining optimal trading strategies. In this paper we describe the constrained mixture model, based on a mixture of Gamma and Gaussian distributions, to provide an accurate…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of…
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
In this paper, we propose finite mixtures of multivariate skew Laplace distributions to model both skewness and heavy-tailedness in the heterogeneous data sets. The maximum likelihood estimators for the parameters of interest are obtained…
In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Log Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape…