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Related papers: Smooth tail index estimation

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Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…

Methodology · Statistics 2016-01-20 John H. J. Einmahl , Anna Kiriliouk , Johan Segers

We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…

Methodology · Statistics 2024-04-05 Bernhard Klar

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…

Machine Learning · Statistics 2010-06-24 Fabian L. Wauthier , Michael I. Jordan

In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has…

Methodology · Statistics 2021-09-28 Cira E. G. Otiniano , Bianca Sousa , Roberto Vila , Marcelo Bourguignon

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…

Statistics Theory · Mathematics 2025-02-18 Martin Bladt , Igor Rodionov

The sum of Log-normal variates is encountered in many challenging applications such as in performance analysis of wireless communication systems and in financial engineering. Several approximation methods have been developed in the…

Statistics Theory · Mathematics 2017-05-29 Mohamed-Slim Alouini , Nadhir Ben Rached , Abla Kammoun , Raul Tempone

This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep…

Statistics Theory · Mathematics 2022-09-02 Wei Huang , Shuo Li , Liuhua Peng

The task of estimation of the tails of probability distributions having small samples seems to be still opened and almost unsolvable. The paper tries to make a step in filling this gap. In 2017 Jordanova et al. introduce six new…

Statistics Theory · Mathematics 2018-11-14 Pavlina Jordanova , Monika Peteva

Global-local shrinkage hierarchies are an important innovation in Bayesian estimation. We propose the use of log-scale distributions as a novel basis for generating familes of prior distributions for local shrinkage hyperparameters. By…

Statistics Theory · Mathematics 2020-01-31 Daniel F. Schmidt , Enes Makalic

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

Probability · Mathematics 2019-01-21 Harry Joe , Haijun Li

Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…

Statistics Theory · Mathematics 2016-06-21 Gaonyalelwe Maribe , Andréhette Verster , Jan Beirlant

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 present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a…

Statistics Theory · Mathematics 2011-08-15 Olivier Catoni

Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…

Methodology · Statistics 2025-07-31 Amenah AL-Najafi , Ugur Tirnakli , Kenric P. Nelson

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…

Statistics Theory · Mathematics 2007-06-13 John H. J. Einmahl , Tao Lin

In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…

Statistics Theory · Mathematics 2016-12-15 J. Martin van Zyl

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

Machine Learning · Statistics 2022-10-11 Takeyuki Sasai

We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…

Methodology · Statistics 2013-11-25 Jinguo Gong , Yadong Li , Liang Peng , Qiwei Yao

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some…

Probability · Mathematics 2024-09-10 M. R. Formica , E. Ostrovsky , L. Sirota

We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.