Related papers: Extreme Value distribution for singular measures
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
Let $(\varepsilon_{t})_{t>0}$ be a sequence of independent real random vectors of $p$-dimension and let $X_T=\sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}/T$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…
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 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…
We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
We give a brief account of application of extreme value theory in dynamical systems by using perturbation techniques associated to the transfer operator. We will apply it to the baker's map and we will get a precise formula for the extremal…
I propose a new procedure to estimate the False Alarm Probability, the measure of significance for peaks of periodograms. The key element of the new procedure is the use of generalized extreme-value distributions, the limiting distribution…
We introduce and study Multi-Quantile estimators for the parameters $( \xi, \sigma, \mu)$ of Generalized Extreme Value (GEV) distributions to provide a robust approach to extreme value modeling. Unlike classical estimators, such as the…
The vanilla method in univariate extreme-value theory consists of fitting the three-parameter Generalized Extreme-Value (GEV) distribution to a sample of block maxima. Despite claims to the contrary, the asymptotic normality of the maximum…
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
In this paper we study extreme value distributions for one-parameter actions on homogeneous spaces of Lie groups. We study both shortest vectors in unimodular lattices, maximal distance excursions and closest distance returns of a…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
In this work, we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu…