Spherical clustering in detection of groups of concomitant extremes

V Fomichov and J Ivanovs

Biometrika, 2023, vol. 110, issue 1, 135-153

Abstract: SummaryThere is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-components clustering algorithm. 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 clustering outperforms $k$-means clustering in the difficult case of weak asymptotic dependence within the groups.

Keywords: Angular measure; Concomitant extreme; Dimension reduction; Mixture model; Principal component (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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