相关论文: Efficient inference about the tail weight in multi…

The minimax risk is often considered as a gold standard against which we can compare specific statistical procedures. Nevertheless, as has been observed recently in robust and heavy-tailed estimation problems, the inherent reduction of the…

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

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 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…

Le Cam's third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic $T_n$ under a non-null sequence of probability measures $\{Q_n\}$, provided its limiting distribution under a null…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…

Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…

The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

Methodologies to test hypotheses about the tail-heaviness of an underlying distribution are introduced based on results of Rojo (1996) using the limiting behavior of the extreme spacings. The tests are consistent and have point-wise robust…

The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…

Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these…

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method…

We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…

This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution…

In the real world, long-tailed data distributions are prevalent, making it challenging for models to effectively learn and classify tail classes. However, we discover that in the field of drug chemistry, certain tail classes exhibit higher…

Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…

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…

Variational inference with {\alpha}-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using {\alpha}-divergences (with positive {\alpha} values) is…