Related papers: Multivariate sparse clustering for extremes
We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator…
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…
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 extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may…
The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
In multivariate extreme value analysis, the estimation of the dependence structure in extremes is demanding, especially in the context of high-dimensional data. Therefore, a common approach is to reduce the model dimension by considering…
Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
Many random phenomena, including life-testing and environmental data, show positive values and excess zeros, which pose modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality,…