Related papers: Semiparametric Exponential Families for Heavy-Tail…
Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
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…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
Statistical modeling of high dimensional extremes remains challenging and has generally been limited to moderate dimensions. Understanding structural relationships among variables at their extreme levels is crucial both for constructing…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
Real-world visual data often exhibits a long-tailed distribution, where some ''head'' classes have a large number of samples, yet only a few samples are available for ''tail'' classes. Such imbalanced distribution causes a great challenge…
We introduce the \textsc{Tailed-Uniform} proposal distribution for generating training simulations in simulation-based inference. Instead of sampling parameters uniformly within bounded regions, we extend the distribution beyond prior…
The problem of class imbalanced data is that the generalization performance of the classifier deteriorates due to the lack of data from minority classes. In this paper, we propose a novel minority over-sampling method to augment diversified…
This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…
Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…