Related papers: Extrapolation in Statistical Learning with Extreme…

When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest…

The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…

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,…

Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…

We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…

Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed datasets while using only minimal assumptions. However, such…

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

Attaining ultra-reliable communication (URC) in fifth-generation (5G) and beyond networks requires deriving statistics of channel in ultra-reliable region by modeling the extreme events. Extreme value theory (EVT) has been previously…

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…

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…

Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the…

We propose a distance supervised relation extraction approach for long-tailed, imbalanced data which is prevalent in real-world settings. Here, the challenge is to learn accurate "few-shot" models for classes existing at the tail of the…

To capture the extremal behaviour of complex environmental phenomena in practice, flexi\-ble techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula…

We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.

The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these…

The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all…

This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…