Related papers: The Probability Conflation: A Reply
In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk…
What do binary (or probabilistic) forecasting abilities have to do with overall performance? We map the difference between (univariate) binary predictions, bets and "beliefs" (expressed as a specific "event" will happen/will not happen) and…
In this paper we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much…
The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation ($CTE$) for a loss distribution with a finite mean but infinite variance. The present work introduces a new…
Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and accordingly unpromising performance especially on tail classes. Recently, the ensembling based methods achieve the…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
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,…
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…
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…
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…
Extreme weather events are becoming more frequent and intense, posing serious threats to human life, biodiversity, and ecosystems. A key objective of extreme event attribution (EEA) is to assess whether and to what extent anthropogenic…