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Related papers: Several new tail index estimators

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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.…

Statistics Theory · Mathematics 2020-03-02 Amenah AL-Najafi , László Viharos

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…

Computational Finance · Quantitative Finance 2012-01-24 Jozef Barunik , Lukas Vacha

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…

Statistics Theory · Mathematics 2014-04-10 Stéphan Clémençon , Antoine Dematteo

We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for…

Probability · Mathematics 2016-01-27 Peter Tankov

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…

Statistics Theory · Mathematics 2020-10-09 John H. J. Einmahl , Johan Segers

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…

Statistics Theory · Mathematics 2018-02-06 Brahim Brahimi , Djamel Meraghni , Abdelhakim Necir , Louiza Soltane

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

Methodology · Statistics 2025-11-27 Ioannis Kalogridis , Stanislav Nagy

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…

Statistics Theory · Mathematics 2011-03-31 Laurent Gardes , Stéphane Girard

The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the…

Methodology · Statistics 2022-12-19 Nan Zou

Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…

Applications · Statistics 2015-02-26 Danang Teguh Qoyyimi , Ricardas Zitikis

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…

Methodology · Statistics 2013-10-02 Danijel Grahovac , Mofei Jia , Nikolai N. Leonenko , Emanuele Taufer

This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…

Probability · Mathematics 2025-08-19 Hamza Hanbali , Daniel Linders

In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…

Methodology · Statistics 2018-09-19 Thomas Taimre , Patrick J. Laub

We are concerned in this paper with the functional asymptotic behaviour of the sequence of stochastic processes T_{n}(f)=\sum_{j=1}^{j=k}f(j)(\log X_{n-j+1,n}-\log X_{n-j,n}), indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}…

Methodology · Statistics 2016-04-19 Gane Samb Lo , El Hadji Deme

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

Methodology · Statistics 2014-12-11 Holger Drees , Johan Segers , Michał Warchoł

We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…

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…

Statistics Theory · Mathematics 2016-02-16 Brahim Brahimi , Zoubir Kenioua

In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the…

Statistics Theory · Mathematics 2008-11-14 John H. J. Einmahl , Andrea Krajina , Johan Segers

A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…

Data Analysis, Statistics and Probability · Physics 2009-05-20 Éva Rácz , János Kertész , Zoltán Eisler

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

Statistics Theory · Mathematics 2025-06-03 Yannick Baraud , Guillaume Maillard