Dimension reduction in multivariate extreme value analysis

By Emilie Chautru. 2015

54 citations recorded by the source corpus.

Non-parametric assessment of extreme dependence structures between an arbitrary number of variables, though quite well-established in dimension 2 and recently extended to moderate dimensions such as 5, still represents a statistical challenge in larger dimensions. Here, we propose a novel approach that combines clustering techniques with angular/spectral measure analysis to find groups of variables (not necessarily disjoint) exhibiting asymptotic dependence, thereby reducing the dimension of the initial problem. A heuristic criterion is proposed to choose the threshold over which it is acceptable to consider observations as extreme and the appropriate number of clusters. When empirically evaluated through numerical experiments, the approach we promote here is found to be very efficient under some regularity constraints, even in dimension 20. For illustration purpose, we also carry out a case study in dietary risk assessment. MSC 2010 subject classifications: 62H12, 62H30, 62G32.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dd2108a49595afbed8e7851bde19b36d28873954

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Emeric Thibaud
2. Jennifer L. Wadsworth
3. Daniel Cooley
4. Emma S. Simpson
5. Jonathan A. Tawn
6. A. C. Davison
7. Raphaël Huser
8. Thomas Opitz

In Finance

1. Emeric Thibaud
2. Jennifer L. Wadsworth
3. Raphaël Huser
4. A. C. Davison
5. Daniel Cooley
6. Thomas Opitz
7. Emma S. Simpson
8. Jonathan A. Tawn

In Statistics and Probability

1. Daniel Cooley
2. Emma S. Simpson
3. Jonathan A. Tawn
4. Emeric Thibaud
5. Jennifer L. Wadsworth
6. Thomas Opitz
7. Raphaël Huser
8. Chen Zhou

Citations in the corpus

• Decompositions of dependence for high-dimensional extremes (2016, background): “M E ] determine a max-stable model from pairwise and higher-dimensional summaries of extremal dependence, and Chautru (2015) who proposes a clustering approach to group variables.”
• Determining the dependence structure of multivariate extremes (2018, methodology): “Chautru (2015) introduces a non-parametric approach based on statistical learning, combining a principal component analysis algorithm with clustering techniques.”