Related papers: A new method for estimating the tail index using t…
A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the traditional Hill estimator, building upon a layered structure…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…
In this paper we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish its strong…
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 present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation ($CTE$) for a loss distribution with a finite mean but infinite variance. The present work introduces a new…
Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become…
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…
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…
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…
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…
Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $\alpha$ quantifying tail heaviness. We propose a new semiparametric estimator for $\alpha$ that leverages the two-sum…
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…
In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under {\alpha}-stable distributions. Using large Monte Carlo…
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…