Related papers: Geometric extremal graphical models and coefficien…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…
We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Extremal graphical models encode the conditional independence structure of multivariate extremes and provide a powerful tool for quantifying the risk of rare events. Prior work on learning these graphs from data has focused on the setting…
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to…
Extremal problems involving independent sets are much studied. Two of the most important extremal problems in this context are concerned with the sharp upper bounds for the number of independent sets of fixed size and the independence…
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…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…