Extremal independence old and new

Statistical inference for heavy tailed series with extremal independence

We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to infinity, the conditional distribution of $X_h$ suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the normalization and of the limiting distribution.

Heavy tailed time series with extremal independence

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information about limiting behavior of time series with extremal independence by introducing a sequence of scaling functions and conditional scaling exponent. Both quantities provide more information about joint extremes than a widely used tail dependence coefficient. We calculate the scaling …

通过模函数研究Hüsler-Reiss分布的极值条件独立性

Extremal conditional independence for Hüsler-Reiss distributions via modular functions

本文通过引入两个集合函数和模ularity关系，研究Hüsler-Reiss分布的极值条件独立性，并探讨其在高维极值统计中的应用。

Extremal behavior of pMAX processes

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 a more general multivariate model comprising asymptotic dependence and independence, which has the extended M4 class as a particular case. We study properties of the proposed model. In particular, we compute the multivariate extremal index, tail dependence and extremal coefficients.

Extremal dependence of random scale constructions

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of vectors with a random scale construction $(X_1,X_2)=R(W_1,W_2)$, with non-degenerate $R>0$ independent of $(W_1,W_2)$. Focusing on the presence and strength of asymptotic tail dependence, as express…

Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges

We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which converges almost surely toward that edge and fluctuates according to the Tracy-Widom law at the scale $N^{2/3}$. Moreover, given several generic positive edges, we establish that the associated extremal ei…