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Related papers: Tail inference using extreme U-statistics

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In this paper, we prove exponential tail bounds for canonical (or degenerate) $U$-statistics and $U$-processes under exponential-type tail assumptions on the kernels. Most of the existing results in the relevant literature often assume…

Statistics Theory · Mathematics 2025-04-22 Abhishek Chakrabortty , Arun K. Kuchibhotla

The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…

Methodology · Statistics 2024-11-22 Yiwei Tang , Judy Huixia Wang , Deyuan Li

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

Methodology · Statistics 2015-02-26 Rafał Kulik , Zhigang Tong

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

Methodology · Statistics 2023-12-18 Liujun Chen , Deyuan Li , Chen Zhou

In several different fields, there is interest in analyzing the upper or lower tail quantile of the underlying distribution rather than mean or center quantile. However, the investigation of the tail quantile is difficult because of data…

Statistics Theory · Mathematics 2019-03-21 Takuma Yoshida

In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…

Methodology · Statistics 2011-04-01 Jean Diebolt , Laurent Gardes , Stéphane Girard , Armelle Guillou

We establish exponential inequalities and Cramer-type moderate deviation theorems for a class of V-statistics under strong mixing conditions. Our theory is developed via kernel expansion based on random Fourier features. This type of…

Statistics Theory · Mathematics 2019-02-08 Yandi Shen , Fang Han , Daniela Witten

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…

Methodology · Statistics 2022-07-26 Yongxin Li , Liujun Chen , Deyuan Li , Hansheng Wang

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

Statistics Theory · Mathematics 2026-04-02 Axel Bücher , Yeonjoon Choi , Katharina Effertz , Stanislav Volgushev

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…

Statistics Theory · Mathematics 2019-07-23 Holger Drees , Miran Knezevic

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

Statistics Theory · Mathematics 2019-02-20 Thomas Lugrin , Anthony C. Davison , Jonathan A. Tawn

We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…

Statistics Theory · Mathematics 2023-01-27 Ioannis Papastathopoulos , Adrian Casey , Jonathan A. Tawn

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…

Statistics Theory · Mathematics 2022-11-28 Natalia Markovich

Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…

Methodology · Statistics 2026-03-17 Bikramjit Das , Xiangyu Liu

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

Machine Learning · Statistics 2026-05-05 Sebastian Engelke , Nicola Gnecco , Anne Sabourin

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

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…

Statistics Theory · Mathematics 2021-03-16 Holger Drees , Anja Janßen , Sebastian Neblung

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

Probability · Mathematics 2019-07-23 Pavlina Jordanova

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…

Statistical Finance · Quantitative Finance 2019-02-26 Chiara Lattanzi , Manuele Leonelli

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…

Statistics Theory · Mathematics 2011-04-04 L. Gardes , S. Girard , A. Lekina