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Related papers: Testing for tail behavior using extreme spacings

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Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not…

Statistics Theory · Mathematics 2016-08-24 Zacharie Naulet , Judith Rousseau

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…

Statistical Mechanics · Physics 2013-02-19 S. I. Denisov , Yu. S. Bystrik , H. Kantz

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

Statistics Theory · Mathematics 2007-06-13 Peter Hall , Ingrid Van Keilegom

We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification…

Methodology · Statistics 2021-08-11 Miguel de Carvalho , Soraia Pereira , Paula Pereira , Patrícia de Zea Bermudez

We discuss an "operational" approach to testing convex composite hypotheses when the underlying distributions are heavy-tailed. It relies upon Euclidean separation of convex sets and can be seen as an extension of the approach to testing by…

Statistics Theory · Mathematics 2018-11-13 Vincent Guigues , Anatoli Juditsky , Arkadi Nemirovski

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…

Statistics Theory · Mathematics 2008-06-27 Yuval Nardi , David O. Siegmund , Benjamin Yakir

Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…

Statistics Theory · Mathematics 2007-06-13 John H. J. Einmahl , Laurens de Haan , Deyuan Li

The block maxima method is one of the most popular approaches for extreme value analysis with independent and identically distributed observations in the domain of attraction of an extreme value distribution. The lack of a rigorous study on…

Methodology · Statistics 2022-04-12 Simone A Padoan , Stefano Rizzelli

This note presents an operational measure of fat-tailedness for univariate probability distributions, in $[0,1]$ where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size…

Methodology · Statistics 2019-04-30 Nassim Nicholas Taleb

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…

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

We study the high-dimensional uniformity testing problem, which involves testing whether the underlying distribution is the uniform distribution, given $n$ data points on the $p$-dimensional unit hypersphere. While this problem has been…

Statistics Theory · Mathematics 2025-06-03 Tiefeng Jiang , Tuan Pham

``Localization'' has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem geometry. Localized bounds seem to be much less exploited in the Stochastic Optimization…

Optimization and Control · Mathematics 2023-03-30 Roberto I. Oliveira , Philip Thompson

In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…

Probability · Mathematics 2023-06-21 Prakirt Raj Jhunjhunwala , Daniela Hurtado-Lange , Siva Theja Maguluri

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

Statistics Theory · Mathematics 2026-05-14 Debanjana Datta , Diganta Mukherjee

In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…

Statistics Theory · Mathematics 2007-08-07 Tucker McElroy , Dimitris N. Politis

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…

Machine Learning · Computer Science 2025-10-14 Yunlong Feng , Qiang Wu

The G-normal distribution was introduced by Peng [2007] as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we…

Statistics Theory · Mathematics 2019-09-10 Shige Peng , Quan Zhou

The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…

Probability · Mathematics 2017-12-12 Svante Janson , Lutz Warnke

Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…

Statistics Theory · Mathematics 2023-05-29 Samuel Valiquette , Gwladys Toulemonde , Jean Peyhardi , Éric Marchand , Frédéric Mortier