Related papers: Sharp moment and exponential tail estimates for U-…

In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and…

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal…

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…

The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments…

We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with non-negligible probability. We propose to combine a two-step procedure for…

This paper presents a new, short proof of the computation of the upper tail large deviation rate function for the Brownian directed percolation model. Through a distributional equivalence between the last passage time in this model and the…

The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the…

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations.…

We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…

In this paper, we obtain optimal uniform lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12]. The…

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

We show that the full-sample bootstrap is asymptotically valid for constructing confidence intervals for high-quantiles, tail probabilities, and other tail parameters of a univariate distribution. This resolves the doubts that have been…

We derive two-sided estimates for random multilinear forms (random chaoses) generated by independent symmetric random variables with logarithmically concave tails. Estimates are exact up to multiplicative constants depending only on the…

We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…

We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high…

We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative…