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This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

For a large $n\times m$ Gaussian matrix, we compute the joint statistics, including large deviation tails, of generalized and total variance - the scaled log-determinant $H$ and trace $T$ of the corresponding $n\times n$ covariance matrix.…

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large…

We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any…

Long-tailed learning has attracted much attention recently, with the goal of improving generalisation for tail classes. Most existing works use supervised learning without considering the prevailing noise in the training dataset. To move…

In this paper, we revisit the proof of the large deviations principle of Wiener chaoses partially given by Borel, and then by Ledoux in its full form. We show that some heavy-tail phenomena observed in large deviations can be explained by…

Noisy labels, which are common in real-world datasets, can significantly impair the training of deep learning models. However, recent adversarial noise-combating methods overlook the long-tailed distribution of real data, which can…

Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…

We analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex with the same convexity parameter for each realization.…

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative…

Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail…

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…