Pandolfo, Giuseppe; Paindaveine, Davy; Porzio, Giovanni C. Distance-based depths for directional data. (English. French summary) Zbl 1492.62095 Can. J. Stat. 46, No. 4, 593-609 (2018). Summary: Directional data are constrained to lie on the unit sphere of \(\mathbb{R}^{q}\) for some \(q \geq 2\). To address the lack of a natural ordering for such data, depth functions have been defined on spheres. However, the depths available either lack flexibility or are so computationally expensive that they can only be used for very small dimensions \(q\). In this work, we improve on this by introducing a class of distance-based depths for directional data. Irrespective of the distance adopted, these depths can easily be computed in high dimensions too. We derive the main structural properties of the proposed depths and study how they depend on the distance used. We discuss the asymptotic and robustness properties of the corresponding deepest points. We show the practical relevance of the proposed depths in two applications, related to (i) spherical location estimation and (ii) supervised classification. For both problems, we show through simulation studies that distance-based depths have strong advantages over their competitors. Cited in 10 Documents MSC: 62H11 Directional data; spatial statistics 62G20 Asymptotic properties of nonparametric inference Keywords:arc distance depth; chord distance depth; cosine distance depth; hyperspheres; spherical location; statistical depth; supervised classification PDFBibTeX XMLCite \textit{G. Pandolfo} et al., Can. J. Stat. 46, No. 4, 593--609 (2018; Zbl 1492.62095) Full Text: DOI arXiv