Related papers: On tail inference in iid settings with nonnegative…
The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail…
Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when…
In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and…
We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
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…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
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,…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However,…
Ratios of central order statistics seem to be very useful for estimating the tail of the distributions and therefore, quantiles outside the range of the data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three…
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…
We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…
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…
Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically…