Related papers: Regression estimator for the tail index

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…

The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…

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…

A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…

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…

A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of…

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

In the paper we propose some new class of functions which is used to construct tail index estimators. Functions from this new class is non-monotone in general, but presents a product of two monotone functions: the power function and the…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

We use the so-called t-Hill tail index estimator proposed by Fabi\'an(2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of loss. Under the second-order condition of regular variation, we establish…

Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we…

In a companion paper (McRobie(2013) arxiv:1304.3918), a simple set of `elemental' estimators was presented for the Generalized Pareto tail parameter. Each elemental estimator: involves only three log-spacings; is absolutely unbiased for all…

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…

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…

When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…

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…

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…