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In this paper, we study the asymptotic behaviors of the extreme of mixed skew-t distribution. We considered limits on distribution and density of maximum of mixed skew-t distribution under linear and power normalization, and further derived…
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…
A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes many…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable…
The statistics of peaks in weak gravitational lensing maps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…
This note studies the asymptotic properties of the variable $$Z_d:=\frac{X_1}{d}|\{X_1+X_2=d\},$$ as $d\to \infty$. Here $X_1$ and $X_2$ are non-negative i.i.d. variables with a common twice differentiable density function $f$. General…
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in…