Related papers: Some variations on the extremal index
We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the algebraic point of view of our recent work on Popa groups.
Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…
The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the…
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…
Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However,…
The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the…
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…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional…
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…
The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting…
The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme…