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The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has…

Methodology · Statistics 2020-07-20 Simone A. Padoan , Gilles Stupfler

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

Methodology · Statistics 2017-11-15 Shrijita Bhattacharya , Michael Kallitsis , Stilian Stoev

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

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…

Machine Learning · Computer Science 2026-05-14 Hamza Cherkaoui , Hélène Halconruy , Antonio Ocello

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…

Methodology · Statistics 2024-01-25 Qiang Sun

This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…

Machine Learning · Statistics 2022-08-01 Elena Ehrlich , Laurent Callot , François-Xavier Aubet

Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are…

Machine Learning · Computer Science 2023-03-22 Bolian Li , Ruqi Zhang

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

Statistics Theory · Mathematics 2014-10-09 Jianqing Fan , Quefeng Li , Yuyan Wang

The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…

Probability · Mathematics 2015-07-29 Lev B Klebanov , Irina V Volchenkova

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient…

Data Structures and Algorithms · Computer Science 2021-01-20 Samuel B. Hopkins , Jerry Li , Fred Zhang

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…

Methodology · Statistics 2022-11-18 Surya T Tokdar , Sheng Jiang , Erika L Cunningham

We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of…

Statistics Theory · Mathematics 2024-06-03 Urte Adomaityte , Leonardo Defilippis , Bruno Loureiro , Gabriele Sicuro

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose $(1+\epsilon)$-th moment is bounded for some $\epsilon\in (0,1]$. Although there exist methods for generalized linear bandits, most of them…

Machine Learning · Computer Science 2023-10-31 Bo Xue , Yimu Wang , Yuanyu Wan , Jinfeng Yi , Lijun Zhang

A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…

Computation · Statistics 2018-01-03 Henry Lam , Clementine Mottet

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying…

Machine Learning · Computer Science 2014-10-23 Shahar Mendelson

This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…

Statistics Theory · Mathematics 2023-07-27 Junren Chen , Michael K. Ng , Di Wang

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…

Statistics Theory · Mathematics 2020-02-11 Mohamed Laidi , Abdelaziz Rassoul , Hamid Ould Rouis

It was shown that when one disposes of a parametric information of the truncation distribution, the semiparametric estimator of the distribution function for truncated data (Wang, 1989) is more efficient than the nonparametric one. On the…

Statistics Theory · Mathematics 2021-06-03 Saida Mancer , Abdelhakim Necir , Souad Benchaira

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…

Machine Learning · Statistics 2025-05-06 Mert Gurbuzbalaban , Yuanhan Hu , Umut Simsekli , Kun Yuan , Lingjiong Zhu

We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…

Econometrics · Economics 2024-01-25 Sander Barendse