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Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…

Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed distribution $F$, i.e. such that the common distribution of the excesses over a high threshold $u_n$ can be approximated by a Generalized Pareto Distribution…

The ideas of model averaging are used to find weights in peak-over-threshold problems using a possible range of thresholds. A range of the largest observations are chosen and considered as possible thresholds, each time performing…

Manski's nonparametric bounds partially identify the average treatment effects (ATEs) under minimal assumptions, yielding an interval-valued estimand with endpoints that depend on the outcome support - typically treated as known or fixed.…

Accurately quantifying tail risks-rare but high-impact events such as financial crashes or extreme weather-is a central challenge in risk management, with serially dependent data. We develop a Bayesian framework based on the Generalized…

Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…

Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…

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…

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

We study the problem of constructing honest and adaptive confidence intervals for the tail coefficient in the second order Pareto model, when the second order coefficient is unknown. This problem is translated into a testing problem on the…

Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these…

Bayesian composite likelihood estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed under Jeffrey's prior…

Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the…

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…

In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for…

Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…

A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…

Heavy-tailed metrics are common and often critical to product evaluation in the online world. While we may have samples large enough for Central Limit Theorem to kick in, experimentation is challenging due to the wide confidence interval of…

Membership inference attacks (MIAs) have emerged as the standard tool for evaluating the privacy risks of AI models. However, state-of-the-art attacks require training numerous, often computationally expensive, reference models, limiting…