Related papers: Trimming the Hill estimator: robustness, optimalit…

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

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…

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…

We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…

Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we…

We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…

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.…

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…

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

Heavy-tailed metrics are common and often critical to product evaluation in the online world. While we may have samples large enough for Central Limit Theorem to kick in, experimentation is challenging due to the wide confidence interval of…

We address the challenge of performing Targeted Maximum Likelihood Estimation (TMLE) after an initial Highly Adaptive Lasso (HAL) fit. Existing approaches that utilize the data-adaptive working model selected by HAL-such as the relaxed HAL…

Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the…

In this article, we introduce a new variable selection technique through trimming for finite mixture of regression models. Compared to the traditional variable selection techniques, the new method is robust and not sensitive to outliers.…

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,…

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…

In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…

We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We model the tail of the small sample as an…