Dimension-invariant uniform consistency of the empirical spatial distribution function and its associated spatial depth estimator

arXiv:2607.16092 · math.ST, math.PR, stat.ML · Submitted 2026-07-17 · Read on arXiv

Felix Gnettner, Hyemin Yeon, Piotr Kokoszka

math.ST, math.PR, stat.ML

Submitted: 2026-07-17

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Consistency — 7× in this paper · explained in 3 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 14 episodes
• Sample Complexity — 2× in this paper · explained in 20 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• ReLU Network — 1× in this paper · explained in 2 episodes

Sources

• Spatial depth characterizes probability measures

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