Related papers: Estimating the extremal index through local depend…
We investigate a family of multiple-stable processes that may exhibit either long-range or short-range dependence, depending on the parameters. There are two parameters for the processes, the memory parameter $\beta\in(0,1)$ and the…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
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…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…
Non-stationary approximations of the final value of a converging sequence are discussed, and we show that extremal eigenvalues can be reasonably estimated from the CG iterates without much computation at all. We introduce estimators of…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
In this paper, we establishe the extremal bounds of the topological indices -- Sigma index -- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index, which is known $\sigma(G)=\sum_{uv\in…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…
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…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…
We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal…
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…
We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$…
Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…