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In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
To capture the extremal behaviour of complex environmental phenomena in practice, flexi\-ble techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula…
The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
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…
On the occasion of Laurens de Haan's 70th birthday, we discuss two aspects of the statistical inference on the extreme value behavior of time series with a particular emphasis on his important contributions. First, the performance of a…
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…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
We introduce a novel bivariate copula model able to capture both the central and tail dependence of the joint probability distribution. Model that can capture the dependence structure within the joint tail have important implications in…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and…
We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…
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…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…