Related papers: A new estimator for the tail-dependence coefficien…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
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,…
We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…
Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
Extreme events are often multivariate in nature. A compound extreme occurs when a combination of variables jointly produces a significant impact, even if individual components are not necessarily marginally extreme. Compound extremes have…
The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
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…
Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the…