Related papers: Singularity analysis for heavy-tailed random varia…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations…
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…
A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii)…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
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…
We present a new class of prior measures in connection to $\ell_p$ regularization techniques when $p \in(0,1)$ which is based on the generalized Gamma distribution. We show that the resulting prior measure is heavy-tailed, non-convex and…
We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed…
Independent component analysis (ICA) is the problem of efficiently recovering a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$ where $S \in \mathbb{R}^n$ is a random vector with mutually independent coordinates.…
We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930],…
We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative numerical integration of linear convolutions by means of…
Anomaly detection methods are widely used but often rely on ad hoc rules or strong assumptions, and they often focus on tail events, missing ``inlier'' anomalies that occur in low-density gaps between modes. We propose a unified framework…
This work is devoted to a vast extension of Sanov's theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a…
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…
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…
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…
Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…
We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…