Related papers: Rare tail approximation using asymptotics and $L^1…
In this paper, we consider the tail probabilities of extremals of $\beta$-Jacobi ensemble which plays an important role in multivariate analysis. The key steps in constructing estimators rely on the rate functions of large deviations.…
Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not…
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…
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…
This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample…
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 paper investigates the second order asymptotic expansion for tail probabilities of discounted aggregate claims in continuous-time renewal risk models with constant interest force. Concretely, two types of continuous-time renewal risk…
Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
Correcting for skewness can result in more accurate tail probability approximations in the central limit theorem for sums of independent random variables. In this paper, we extend the theory to sums of local statistics of independent random…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
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…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…
The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the…
Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
Long-tail learning has garnered widespread attention and achieved significant progress in recent times. However, even with pre-trained prior knowledge, models still exhibit weaker generalization performance on tail classes. The promising…
In this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…