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The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…

Methodology · Statistics 2025-05-05 Emma S. Simpson , Jonathan A. Tawn

The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…

Statistics Theory · Mathematics 2009-06-12 Moosup Kim , Sangyeol Lee

We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…

Methodology · Statistics 2020-06-30 Martin Bladt , Hansjoerg Albrecher , Jan Beirlant

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

Applications · Statistics 2025-03-19 Jialin Zhang , Zhiyi Zhang

Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…

Methodology · Statistics 2018-12-17 Anna Kiriliouk

Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from…

Statistics Theory · Mathematics 2013-12-19 Abdelaati Daouia , Laurent Gardes , Stéphane Girard

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

Statistics Theory · Mathematics 2026-04-14 John H. J. Einmahl , Chen Zhou

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…

Methodology · Statistics 2019-12-06 Shrijita Bhattacharya , Jan Beirlant

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

Statistics Theory · Mathematics 2024-01-02 Zhiyuan Huang , Henry Lam , Zhenyuan Liu

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…

Probability · Mathematics 2022-12-05 Anja Janßen , Sebastian Neblung , Stilian Stoev

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

Probability · Mathematics 2018-02-05 Ulrich K. Mueller

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…

Econometrics · Economics 2020-02-25 Yulong Wang , Zhijie Xiao

Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…

Statistics Theory · Mathematics 2016-06-30 Paul Rochet , Isabel Serra

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

Statistics Theory · Mathematics 2018-04-19 Cheng Li , Lizhen Lin , David B. Dunson

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…

Methodology · Statistics 2026-05-20 Jonas F. Frederiksen , Muneya Matsui , Rasmus S. Pedersen

On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent…

Statistics Theory · Mathematics 2016-07-25 Brahim Brahimi , Djamel Meraghni , Abdelhakim Necir

We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to…

Applications · Statistics 2016-09-05 Pasquale Cirillo , Nassim Nicholas Taleb

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method…

Methodology · Statistics 2023-07-25 Matthieu Garcin , Maxime L. D. Nicolas

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…

Statistics Theory · Mathematics 2021-10-15 Abdelhakim Necir , Louiza Soltane

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…

Data Analysis, Statistics and Probability · Physics 2019-06-24 Pablo Lopez Rios , Gareth J. Conduit