Horospherical depth generalizes Tukey's half-space depth to Hadamard manifolds via Busemann functions, producing a Busemann median with nested convex depth regions, a 1/(d+1) centerpoint guarantee, and robustness to contamination at infinity.
A theorem on general measure.Journal of the London Mathematical Society 1291–300
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Horospherical Depth and Busemann Median on Hadamard Manifolds
Horospherical depth generalizes Tukey's half-space depth to Hadamard manifolds via Busemann functions, producing a Busemann median with nested convex depth regions, a 1/(d+1) centerpoint guarantee, and robustness to contamination at infinity.