mlsanityData to 13 Oct 2026

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

arXiv 2607.16092 ↗First posted 17 Jul 2026math.ST math.PR stat.MLcited by 0

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Abstract (arXiv)

We provide a proof that the empirical spatial distribution estimator in mathbb Rd as well as the corresponding plug-in estimator of the spatial depth are uniformly L1-consistent. The consistency rate only depends on the sample size n, not on the dimension d or any tuning or regularization parameters. This is a rare property. The result of this note originates from a conversation with ChatGPT 5.4 Pro as part of some of our own earlier experiments on its mathematical reasoning capabilities.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 6 of its 20 references that are in the map. First posted on arXiv 17 Jul 2026.

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References · 6

  1. 2017Size-Independent Sample Complexity of Neural Networkscited by 289
  2. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  3. 2023On Size-Independent Sample Complexity of ReLU Networkscited by 6
  4. 2014On data depth in infinite dimensional spacescited by 2
  5. 2014The spatial distribution in infinite dimensional spaces and related quantiles and depthscited by 2
  6. 2023Regularized Halfspace Depth for Functional Datacited by 2

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