Detection of groups of concomitant extremes using clustering
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There is a growing empirical evidence that the spherical k-means clustering performs remarkably well in identification of groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide first theoretical results supporting this approach, but also identify some pitfalls. Furthermore, we develop a novel spherical k-principal-components clustering algorithm which is more appropriate for identification of concomitant extremes. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method, albeit in a rather basic setting. Finally, we illustrate in simulations that k-principal-components outperforms k-means in the difficult case of weak asymptotic dependence within the groups.
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