Related papers: Smooth tail index estimation

Score estimation has recently emerged as a key modern statistical challenge, due to its pivotal role in generative modelling via diffusion models. Moreover, it is an essential ingredient in a new approach to linear regression via convex…

Semantic segmentation usually suffers from a long-tail data distribution. Due to the imbalanced number of samples across categories, the features of those tail classes may get squeezed into a narrow area in the feature space. Towards a…

Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However,…

Let $X_{1,n}\le\cdots\le X_{n,n}$ be the order statistics of $n$ independent random variables with a common distribution function $F$ having right heavy tail with tail index $\gamma$. Given known constants $d_{i,n}$, $1\le i\le n$, consider…

We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…

We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…

This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…

We introduce a new actuarial tail-shape index, the $\theta$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for…

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

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…

We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially-varying effects of covariates on the quantile function. By modeling the quantile function as a combination of I-spline basis…

In this paper, we propose an estimator of the second-order parameter of randomly right-truncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

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…

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…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…