Related papers: Perturbation-based Inference for Extreme Value Ind…
One of the main topics of extreme value analysis is to estimate the extreme value index, an important parameter that controls the tail behavior of the distribution. In many cases, estimating the extreme value index of the target variable…
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…
Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is…
This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…
Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
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 consider the problem of evaluating risk for a system that is modeled by a complex stochastic simulation with many possible input parameter values. Two sources of computational burden can be identified: the effort associated with…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…
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…
Ultra-reliable low-latency communications (URLLC) require innovative approaches to modeling channel and interference dynamics, extending beyond traditional average estimates to encompass entire statistical distributions, including rare and…
Inference in extreme value theory relies on a limited number of extreme observations, making estimation challenging. To address this limitation, we propose a non-parametric simulation scheme, the multivariate extreme events spectral…
We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process:…
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions…
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…
A variety of methods have been proposed to try to explain how deep neural networks make their decisions. Key to those approaches is the need to sample the pixel space efficiently in order to derive importance maps. However, it has been…
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…
Understanding multivariate extreme events play a crucial role in managing the risks of complex systems since extremes are governed by their own mechanisms. Conditional on a given variable exceeding a high threshold (e.g.\ traffic…
In a companion paper (McRobie(2013) arxiv:1304.3918), a simple set of `elemental' estimators was presented for the Generalized Pareto tail parameter. Each elemental estimator: involves only three log-spacings; is absolutely unbiased for all…
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP)…