Related papers: Some variations on the extremal index
Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we…
We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e.…
In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…
In multivariate extreme value statistics, the first step in understanding the dependence structure of extremes is identifying the directions in which they occur. The novelty of this paper is the analysis of high-dimensional extreme value…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
In this work, we focus on some conditional extreme risk measures estimation for elliptical random vectors. In a previous paper, we proposed a methodology to approximate extreme quantiles, based on two extremal parameters. We thus propose…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
Extreme events are a major concern in statistical modeling. Ran\-dom missing data can constitute a problem when modeling such rare events. Imputation is crucial in these situations and therefore models that describe different imputation…
In extreme value analysis, the extreme value index plays a vital role as it determines the tail heaviness of the underlying distribution and is the primary parameter required for the estimation of other extreme events. In this paper, we…
Accurate estimation of the frequency and magnitude of successive extreme events in energy demand is critical for strategic resource planning. Traditional approaches based on extreme value theory (EVT) are typically limited to modelling…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…
The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in…
This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals…
Stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of Markov random fields restricted to one dimension. Non stationary reciprocal processes have been extensively studied in the…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
This paper studies extremal quantiles under two-way clustered dependence. We show that the limiting distribution of unconditional intermediate-order tail quantiles is Gaussian. This result is notable because two-way clustering typically…