Related papers: POT-flavored estimator of Pickands dependence func…
We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these…
Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value…
The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the…
Pickands dependence functions characterize bivariate extreme value copulas. In this paper, we study the class of polynomial Pickands functions. We provide a solution for the characterization of such polynomials of degree at most $m+2$,…
We study the characteristics of the Pickands' dependence function for bivariate extreme distribution for minima, BEVM, when considering the stochastics ordering of the two variables. The existing Pickand's dependence function terminologies…
Consider a continuous random pair $(X,Y)$ whose dependence is characterized by an extreme-value copula with Pickands dependence function $A$. When the marginal distributions of $X$ and $Y$ are known, several consistent estimators of $A$ are…
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…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
Second order conditions provide a natural framework for establishing asymptotic results about estimators for tail related quantities. Such conditions are typically tailored to the estimation principle at hand, and may be vastly different…
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 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…
Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and the peak-over-threshold (POT) approach. It seems to be general consensus among researchers in the field that the POT method makes…
Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for…
The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are…
We describe a puzzle involving the interactions between an optimization of a multivariate quadratic function and a "plug-in" estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) diverge with the…
We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function $A^*(t)$, which minimizes a weighted $L^2$-distance…
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the…
In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper…
The extremal index parameter theta characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance and…
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance…