Related papers: Testing Tail Weight of a Distribution Via Hazard R…

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…

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

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…

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…

Real-world data are long-tailed, the lack of tail samples leads to a significant limitation in the generalization ability of the model. Although numerous approaches of class re-balancing perform well for moderate class imbalance problems,…

How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but…

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…

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 propose a simple data model inspired from natural data such as text or images, and use it to study the importance of learning features in order to achieve good generalization. Our data model follows a long-tailed distribution in the…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

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…