Related papers: Extreme value copula estimation based on block max…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
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…
The block maxima method is a standard approach for analyzing the extremal behavior of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved…
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying…
The block maxima (BM) approach in extreme value analysis fits a sample of block maxima to the Generalized Extreme Value (GEV) distribution. We consider all potential blocks from a sample, which leads to the All Block Maxima (ABM) estimator.…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…
The extreme value index is a fundamental parameter in univariate Extreme Value Theory (EVT). It captures the tail behavior of a distribution and is central in the extrapolation beyond observed data. Among other semi-parametric methods (such…
Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over disjoint blocks of observations.…
We show that all multivariate Extreme Value distributions, which are the possible weak limits of the $K$ largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through…
The maximum likelihood method offers a standard way to estimate the three parameters of a generalized extreme value (GEV) distribution. Combined with the block maxima method, it is often used in practice to assess the extreme value index…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…