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We introduce $\zeta$- and $s$-values as quantile-based standardizations that are particularly suited for hypothesis testing. Unlike p-values, which express tail probabilities, $s$-values measure the number of semi-tail units into a…

Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference distribution. This enables us to give concrete conditions to…

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 article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…

In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under {\alpha}-stable distributions. Using large Monte Carlo…

Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…

We introduce a new rule-based optimization method for classification with constraints. The proposed method leverages column generation for linear programming, and hence, is scalable to large datasets. The resulting pricing subproblem is…

This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk matrix in the case of larger number of time series observations than assets in a…

We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of…

Many real-world classification problems, such as plant identification, have extremely long-tailed class distributions. In order for prediction sets to be useful in such settings, they should (i) provide good class-conditional coverage,…

Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…

This paper contributes to answering a question that is of crucial importance in risk management and extreme value theory: How to select the threshold above which one assumes that the tail of a distribution follows a generalized Pareto…

We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…

The goodness-of-fit test for discrimination of two tail distribution using higher order statistics is proposed. The consistency of proposed test is proved for two different alternatives. We do not assume belonging the corresponding…

Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…

To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…

``When a measure becomes a target, it ceases to be a good measure'', this adage is known as {\it Goodhart's law}. In this paper, we investigate formally this law and prove that it critically depends on the tail distribution of the…

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…