Related papers: Tail processes and tail measures: An approach via …
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…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
The task of estimation of the tails of probability distributions having small samples seems to be still opened and almost unsolvable. The paper tries to make a step in filling this gap. In 2017 Jordanova et al. introduce six new…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
A major issue of extreme value analysis is the determination of the shape parameter $\xi$ common to Generalized Extreme Value (GEV) and Generalized Pareto (GP) distributions, which drives the tail behavior, and is of major impact on the…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…
We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into…
Programs with randomization constructs is an active research topic, especially after the recent introduction of martingale-based analysis methods for their termination and runtimes. Unlike most of the existing works that focus on proving…
A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by…
The modelling of multivariate extreme events is important in a wide variety of applications, including flood risk analysis, metocean engineering and financial modelling. A wide variety of statistical techniques have been proposed in the…
We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random…
In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
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…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…