Connecting pairwise spheres by depth: DCOPS

2017/10/06 by Ricardo Fraiman, Fabrice Gamboa, Fraiman, Ricardo +3 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Morphological variations and asymmetry #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1710.02561

openalex publication_date 2017/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the classical notion of the spherical depth in ℝ^k, to the important setup of data on a Riemannian manifold. We show that this notion of depth satisfies a set of desirable properties. For the empirical version of this depth function both uniform consistency and the asymptotic distribution are studied. Consistency is also shown for functional data. The behaviour of the depth is illustrated through several examples for Riemannian manifold data.

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