Related papers: Extreme value statistics for truncated Pareto-type…

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the…

In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…

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…

We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as \c{hi}2 with a high…

Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail…

Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult…

The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…

In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…

We propose a class of weighted least squares estimators for the tail index of a distribution function with a regularly varying upper tail. Our approach is based on the method developed by \cite{Holan2010} for the Parzen tail index.…

We introduce a kernel estimator, to the tail index of a right-censored Pareto-type distribution, that generalizes Worms's one (Worms and Worms, 2014)in terms of weight coefficients. Under some regularity conditions, the asymptotic normality…

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…

Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…

In this short note, I comment on the research of Pisarenko et al. (2014) regarding the extreme value theory and statistics in case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic…

Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…

A key building block in the design of ultra-reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. In this paper, we propose a novel methodology based on…

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

We prove the consistency of the Power-Law Fit PLFit method proposed by Clauset et al.(2009) to estimate the power-law exponent in data coming from a distribution function with regularly-varying tail. In the complex systems community, PLFit…

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…

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…