Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables

Asenova, Stefka; Mazo, Gildas; Segers, Johan

doi:10.1007/s10687-021-00407-5

Cited by 16 publications

(25 citation statements)

References 23 publications

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“…Finally, thanks to the structure of the parameter matrix, it is proved in Proposition 4.6 that all parameters of the limiting Hüsler-Reiss max-stable distribution remain identifiable even when some of the variables are latent, as long as these variables lie on nodes with neighbours in at least three different cliques. This generalizes a similar identifiability claim for trees in Asenova et al (2021).…”

Section: Introductionsupporting

confidence: 85%

“…In Engelke et al (2015), such log-normal limits were found to characterize the domain of attraction of the Hüsler-Reiss max-stable distribution. For our Hüsler-Reiss Markov block graphs, Proposition 4.4 states that the parameter matrix of the max-stable limit has an explicit and elegant form determined by the path sums in the block graph, generalizing a structure found for Markov trees in Segers (2020) and Asenova et al (2021). By Proposition 4.5, the multivariate Pareto distribution associated to the Hüsler-Reiss max-stable distribution is an extremal graphical model with respect to the same graph.…”

Section: Introductionmentioning

confidence: 92%

“…In Asenova et al (2021) a criterion was presented for checking whether the parameters of the Hüsler-Reiss distribution are identifiable if for some of the nodes v ∈ V the variables X v are unobservable (latent). The issue was illustrated for river networks when the water level or another variable of interest is not observed at some splits or junctions.…”

Section: Latent Variables and Parameter Identifiabilitymentioning

confidence: 99%

“…In Section 4, we study the implications of our main convergence result for a Markov block graph in which the joint law on each clique is the max-stable Hüsler-Reiss distribution (Hüsler and Reiss, 1989). This model generalizes the Hüsler-Reiss Markov tree in Asenova et al (2021) used to study extremes of a river network. Note again that by Papastathopoulos and Strokorb (2016), the joint law of such a Markov block graph is itself not a Hüsler-Reiss max-stable distribution.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extremes of Markov random fields on block graphs: max-stable limits and structured Hüsler-Reiss distributions

Asenova¹,

Segers²

2021

Preprint

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We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs, containing trees as special cases, we aim to generalize recent results for extremes of Markov trees. Every pair of nodes in a block graph is connected by a unique shortest path. These paths are shown to determine the limiting distribution of the properly rescaled random field given that a fixed variable exceeds a high threshold.When the sub-vectors induced by the blocks follow Hüsler-Reiss extreme value copulas, the global Markov property of the original field induces a particular structure on the parameter matrix of the limiting max-stable Hüsler-Reiss distribution. The multivariate Pareto version of the latter turns out to be an extremal graphical model according to the original block graph. Moreover, thanks to these algebraic relations, the parameters are still identifiable even if some variables are latent.

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Section: Introductionsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 92%

Section: Latent Variables and Parameter Identifiabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extremes of Markov random fields on block graphs: max-stable limits and structured Hüsler-Reiss distributions

Asenova¹,

Segers²

2021

Preprint

Self Cite

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show abstract

“…analyzing the extremes of a high dimensional random vector. Such studies can be divided into the following categories: clustering methods [6,7,39], support identification, [32,33,8,9,53,44], Principal Component Analysis of the angular component of extremes [14,41,20], and graphical models for extremes [36,23,1]; see also [24] and the references therein. Our approach is remotely related to the last category: extremal graphical models.…”

Section: Dimensionality Reduction In Evtmentioning

confidence: 99%

Tail inverse regression for dimension reduction with extreme response

Aghbalou¹,

Portier²,

Sabourin³

et al. 2021

Preprint

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We consider the problem of dimensionality reduction for prediction of a target Y ∈ R to be explained by a covariate vector X ∈ R p , with a particular focus on extreme values of Y which are of particular concern for risk management. The general purpose is to reduce the dimensionality of the statistical problem through an orthogonal projection on a lower dimensional subspace of the covariate space. Inspired by the sliced inverse regression (SIR) methods, we develop a novel framework (TIREX, Tail Inverse Regression for EXtreme response) relying on an appropriate notion of tail conditional independence in order to estimate an extreme sufficient dimension reduction (SDR) space of potentially smaller dimension than that of a classical SDR space. We prove the weak convergence of tail empirical processes involved in the estimation procedure and we illustrate the relevance of the proposed approach on simulated and real world data.

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On pairwise interaction multivariate Pareto models

Lalancette

2023

Stat

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The rich class of multivariate Pareto distributions forms the basis of recently introduced extremal graphical models. However, most existing literature on the topic is focused on the popular parametric family of Hüsler–Reiss distributions. It is shown that the Hüsler–Reiss family is in fact the only continuous multivariate Pareto model that exhibits the structure of a pairwise interaction model, justifying its use in many high‐dimensional problems. Along the way, useful insight is obtained concerning a certain class of distributions that generalize the Hüsler–Reiss family, a result of independent interest.

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Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables

Cited by 16 publications

References 23 publications

Extremes of Markov random fields on block graphs: max-stable limits and structured Hüsler-Reiss distributions

Extremes of Markov random fields on block graphs: max-stable limits and structured Hüsler-Reiss distributions

Tail inverse regression for dimension reduction with extreme response

On pairwise interaction multivariate Pareto models

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