par Konen, Dimitri 
;Paindaveine, Davy
Référence Annales de l'I.H.P. Probabilités et statistiques, 62, 1, page (548-581)
Publication Publié, 2026-02-01
;Paindaveine, Davy Référence Annales de l'I.H.P. Probabilités et statistiques, 62, 1, page (548-581)
Publication Publié, 2026-02-01
Article révisé par les pairs
| Résumé : | Spatial quantiles are among the most successful concepts of multivariate quantiles. In particular, they are essentially the only quantiles that can be computed in high dimensions. There has been an intense research activity to study spatial quantiles in the last two decades, yet surprisingly little is known about their robustness properties. In the present work, we carefully study the breakdown point of spatial quantiles. We offer three approaches, that show diverse distinctive advantages. The first approach is a constructive one: it is conceptually simple and allows us to derive the finite-sample breakdown point of spatial quantiles. While the second approach is not constructive and does not identify the global breakdown point of spatial quantiles, it provides an upper bound on the breakdown point under contamination in any fixed direction. It also allows us to determine the breakdown point of spatial Lp-quantiles for any p > 1. Last but not least, the third approach characterizes precisely when breakdown occurs under any given contamination scheme, hence provides the breakdown points associated with very diverse contamination scenarios. Quite nicely, this last approach further covers cases where the contamination and/or the ground probability measures are continuous distributions. An intriguing corollary of our results states that, in high dimensions, the “practical” breakdown point exceeds the theoretical one. Throughout, our theoretical results are illustrated through numerical exercises. Part of our results cover infinite-dimensional Hilbert spaces as well. |
