Related papers: Functional Peaks-over-threshold Analysis
In recent years several attempts have been made to extend tail modelling towards the modal part of the data. Frigessi et al. (2002) introduced dynamic mixtures of two components with a weight function {\pi} = {\pi}(x) smoothly connecting…
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an…
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…
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield…
This article extends the multivariate extreme value theory (MEVT) to discrete settings, focusing on the generalized Pareto distribution (GPD) as a foundational tool. The purpose of the study is to enhance the understanding of extreme…
This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
We investigate two models for the following setup: We consider a stochastic process X \in C[0,1] whose distribution belongs to a parametric family indexed by \vartheta \in {\Theta} \subset R. In case \vartheta = 0, X is a generalized Pareto…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of…
A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the…
Deep probabilistic forecasting is gaining attention in numerous applications ranging from weather prognosis, through electricity consumption estimation, to autonomous vehicle trajectory prediction. However, existing approaches focus on…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…
This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching…
Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used…
Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…
The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in…