Related papers: The coupling method in extreme value theory
We give a scheme of using the coupling method to obtain strong bounds for the convergence rate of the distribution of the backward renewal process in the total variation distance. This scheme can be applied to a wide class of regenerative…
Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate…
In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach,…
Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…
Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed distribution $F$, i.e. such that the common distribution of the excesses over a high threshold $u_n$ can be approximated by a Generalized Pareto Distribution…
We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. The recent advances in the methodology of the theory of extreme values is applied to the maximal extremes of the time…
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail…
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…
Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
We develop methods, based on extreme value theory, for analysing observations in the tails of longitudinal data, i.e., a data set consisting of a large number of short time series, which are typically irregularly and non-simultaneously…
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,…
Two automatic threshold selection (TS) methods for Extreme Value analysis under a peaks-over-threshold (POT) approach are presented and evaluated, both built on: fitting the Generalized Pareto distribution (GPd) to excesses' samples over…