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Related papers: Smooth tail index estimation

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We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

Statistics Theory · Mathematics 2024-01-02 Zhiyuan Huang , Henry Lam , Zhenyuan Liu

High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…

Machine Learning · Statistics 2026-01-06 Even He

The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value…

Statistics Theory · Mathematics 2015-07-19 Louiza Soltane , Djamel Meraghni , Abdelhakim Necir

This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be…

Methodology · Statistics 2024-08-22 Martin Bladt , Christoffer Øhlenschlæger

This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…

Econometrics · Economics 2025-02-25 Laura Liu , Yulong Wang

Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…

Machine Learning · Computer Science 2022-04-13 Jacob Deasy , Nikola Simidjievski , Pietro Liò

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…

Numerical Analysis · Mathematics 2020-08-26 Søren Taverniers , Daniel M. Tartakovsky

Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…

Statistics Theory · Mathematics 2017-07-18 Adrien Hitz , Richard Davis , Gennady Samorodnitsky

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,…

Methodology · Statistics 2014-05-09 Brahim Brahimi , Djamel Meraghni , Abdelhakim Necir , Djabrane Yahia

Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible…

Methodology · Statistics 2010-10-05 Guenther Walther

Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…

Statistics Theory · Mathematics 2025-11-10 Hamidreza Maleki Almani

In this paper, we consider a generic scheme that allows building weighted versions of various quantile estimators, such as traditional quantile estimators based on linear interpolation of two order statistics, the Harrell-Davis quantile…

Methodology · Statistics 2023-04-17 Andrey Akinshin

In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized…

Risk Management · Quantitative Finance 2021-03-10 Baishuai Zuo , Chuancun Yin

Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…

Statistics Theory · Mathematics 2009-01-13 Jan Beirlant , Elisabeth Joossens , Johan Segers

Randomized experiments are the gold standard for investigating causal relationships, with comparisons of potential outcomes under different treatment groups used to estimate treatment effects. However, outcomes with heavy-tailed…

Methodology · Statistics 2024-07-09 Hongzi Li , Wei Ma , Yingying Ma , Hanzhong Liu

$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…

Methodology · Statistics 2021-09-14 Kean Ming Tan , Lan Wang , Wen-Xin Zhou

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset…

Condensed Matter · Physics 2016-12-21 Rafal Weron

We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…

Statistics Theory · Mathematics 2026-03-03 Mohammed Es-Salih Benjrada , Cecile Durot , Tommaso Lando

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good…

Methodology · Statistics 2022-08-30 Andrey Akinshin

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Methodology · Statistics 2025-02-24 Liujun Chen , Deyuan Li , Zhengjun Zhang