3 problems

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Non-equivalence of spatial medians and metric spatial Wasserstein depth maximizers
Non-equivalence conjecture. In general, spatial medians have no relation to the maximizers of $\mathrm{MSD}(Q;{\bf P})$ .
Conjectureopenspatial-medians statistical-depth wasserstein-geometryarXiv posted 2 days ago
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The K-means/center stability conjecture for statistical depth-based uncertainty scores
K-means/center stability conjecture. This averaging effect makes the method much more stable and facilitates capturing the overall shape of the cluster by avoiding certain irregula…
Conjectureopenout-of-distribution-detection statistical-depth uncertainty-quantificationarXiv posted 2 days ago
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Determinant dependence conjecture for Tyler shape depth under ellipticity
Determinant dependence conjecture. Irrespective of the dimension $k$ , there is a function $g:\mathbb{R}^+\to[0,1]$ such that
Conjectureopenelliptical-distributions shape-matrices statistical-deptharXiv posted 2 days ago

Non-equivalence of spatial medians and metric spatial Wasserstein depth maximizers