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arXiv · 1704.01503

Multivariate Geometric Expectiles

Klaus Herrmann·Marius Hofert·Melina Mailhot
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Abstract

A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample version is shown to be a consistent estimator. We exemplify their usage as risk measures in a number of multivariate settings, highlighting the influence of varying margins and dependence structures.

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Klaus Herrmann, Marius Hofert, Melina Mailhot. 2017-04-05. Multivariate Geometric Expectiles. https://arxiv.org/abs/1704.01503

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