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Some negative results on extreme multivariate quantiles defined through convex optimisation
Abstract : A discussion of some general properties that a notion of extreme multivariate quantile should satisfy will be given. We will then recall the concept of geometric quantile by transposing the definition of a univariate quantile as a minimiser of a cost function based on the so-called check function to the multivariate case. We shall then argue that extreme versions of these geometric quantiles are not suitable for the extreme-value analysis of a multivariate data set. A particular reason for this is that when the underlying distribution possesses a finite covariance matrix then the magnitude of these quantiles grows at a fixed rate that is independent of the distribution. We shall also discuss an extension of this negative result to the wider class of geometric M-quantiles.
https://hal.archives-ouvertes.fr/hal-01667186
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Tuesday, December 19, 2017 - 10:48:36 AM
Last modification on : Wednesday, November 3, 2021 - 5:12:47 AM
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Tuesday, December 19, 2017 - 10:48:36 AM
Last modification on : Wednesday, November 3, 2021 - 5:12:47 AM