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Related papers: Regression estimator for the tail index

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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

We consider a change-point test based on the Hill estimator to test for structural changes in the tail index of Long Memory Stochastic Volatility time series. In order to determine the asymptotic distribution of the corresponding test…

Statistics Theory · Mathematics 2020-06-05 Annika Betken , Davide Giraudo , Rafał Kulik

This article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…

Statistics Theory · Mathematics 2019-09-09 Paolo Gorgi

Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…

Methodology · Statistics 2017-12-27 Nehla Debbabi , Marie Kratz , Mamadou Mboup

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

Statistics Theory · Mathematics 2025-06-03 Sibsankar Singha , Marie Kratz , Sreekar Vadlamani

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…

Risk Management · Quantitative Finance 2011-12-20 Carlo Marinelli , Stefano d'Addona , Svetlozar T. Rachev

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

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

Machine Learning · Computer Science 2022-02-28 Che-Ping Tsai , Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…

Methodology · Statistics 2015-01-12 John Einmahl , Anna Kiriliouk , Andrea Krajina , Johan Segers

Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper we obtain the optimal pointwise convergence rate for…

Statistics Theory · Mathematics 2020-02-18 Hajo Holzmann , Alexander Meister

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

Applications · Statistics 2025-03-19 Jialin Zhang , Zhiyi Zhang

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…

Probability · Mathematics 2018-08-07 Tiandong Wang , Sidney I. Resnick

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…

Statistics Theory · Mathematics 2022-07-11 Michaël Lalancette , Sebastian Engelke , Stanislav Volgushev

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown…

Statistics Theory · Mathematics 2009-09-29 Tucker McElroy , Dimitris N. Politis

To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…

Methodology · Statistics 2026-02-24 Yuanzhi Li , Shushu Zhang , Xuming He

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

Computational Finance · Quantitative Finance 2017-10-04 Igor Halperin

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

Probability · Mathematics 2020-09-08 Anru R. Zhang , Yuchen Zhou

In this work, we focus on some conditional extreme risk measures estimation for elliptical random vectors. In a previous paper, we proposed a methodology to approximate extreme quantiles, based on two extremal parameters. We thus propose…

Statistics Theory · Mathematics 2018-07-26 Antoine Usseglio-Carleve

The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…

Methodology · Statistics 2021-08-03 Helena Ferreira , Marta Ferreira

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the…

Econometrics · Economics 2020-07-15 Ulrich K. Mueller