Related papers: Tail Analysis without Parametric Models: A Worst-c…

Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…

In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…

In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct…

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood. While…

In this paper we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish its strong…

We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…

In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Log Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape…

Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…

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…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…

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…

Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…

The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…

We re-visit tail the index regressions framework. For linear specifications, we find that the usual full rank condition can fail because conditioning on extreme outcomes causes regressors to degenerate to constants. Taking this into…