Related papers: Upper bounds on the minimum coverage probability o…

We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…

Tail Value-at-Risk (TVaR) is a widely adopted risk measure playing a critically important role in both academic research and industry practice in insurance. In data applications, TVaR is often estimated using the empirical method, owing to…

Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…

Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random…

A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…

Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…

Given the high volatility and susceptibility to extreme events in the cryptocurrency market, forecasting tail risk is of paramount importance. Value-at-Risk (VaR), a quantile-based risk measure, is widely used for assessing tail risk and is…

Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the 2nd kind of error…

Often, it is required to estimate the probability that a quantity such as toxicity level, plutonium, temperature, rainfall, damage, wind speed, wave size, earthquake magnitude, risk, etc., exceeds an unsafe high threshold. The probability…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

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…

Conformal prediction methodology has recently been extended to the covariate shift setting, where the distribution of covariates differs between training and test data. While existing results ensure that the prediction sets from these…

In many practical situations exploratory plots are helpful in understanding tail behavior of sample data. The Mean Excess plot is often applied in practice to understand the right tail behavior of a data set. It is known that if the…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…

Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is…

The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…