
06416784
j
06416784
Chautru, Emilie
Dimension reduction in multivariate extreme value analysis.
Electron. J. Stat. 9, 383418, electronic only (2015).
2015
Sponsored by Institute of Mathematical Statistics (IMS), Beachwood, OH and Bernoulli Society
EN
angular/spectral measure
dimension reduction
latent variable
mixture model
extreme dependence
multivariate extremes
doi:10.1214/15EJS1002
euclid:ejs/1426611768
Summary: Nonparametric assessment of extreme dependence structures between an arbitrary number of variables, though quite wellestablished 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.