Related papers: A remarkable example on clustering of extremes for…
Consider an ergodic measure preserving dynamical system $(T,X,\mu)$, and an observable $\phi:X\to\mathbb{R}$. For the time series $X_n(x)=\phi(T^{n}(x))$, we establish limit laws for the maximum process $M_n=\max_{k\leq n}X_k$ in the case…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes…
We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with…
We consider the two block stochastic block model on $n$ nodes with asymptotically equal cluster sizes. The connection probabilities within and between cluster are denoted by $p_n:=\frac{a_n}{n}$ and $q_n:=\frac{b_n}{n}$ respectively. Mossel…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…
The extremal index $\theta$, a measure of the degree of local dependence in the extremes of a stationary process, plays an important role in extreme value analyses. We estimate $\theta$ semiparametrically, using the relationship between the…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
We study the limiting extremal and cluster point processes of branching Brownian motion. The former records the heights of all extreme values of the process, while the latter records the relative heights of extreme values in a genealogical…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…