Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Huber contamination model
Definition
Given a statistical experiment on (Statistical experiments) and any probability measure on that space (Probability measures and probability spaces), Huber's one-observation contamination law is
The mixture is a probability measure by A convex mixture of probability laws is a probability law. In the sample-size- model, observations are iid from this law (Identical distribution and IID families). A worst-case may be chosen separately for each . This is an iid sampling model, distinct from a fixed gross-error direction and from sample replacement.
Depends on
Used by
- Half-sample replacement prevents covariance-only mean recovery Counterexample
- Contamination-robust expected risk and tail risk Definition
- Gaussian Huber contamination model for covariance estimation Definition
- Bounded sample-mean change under replacements and a common corrupted sample Example
- Exact Bernoulli Huber modulus and indistinguishable mixtures Example
- TV-close laws have identical Huber mixtures at the contamination threshold Lemma
- Huber contamination modulus lower bound for tail risk Theorem
Dependency tree · two levels
10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Mengjie Chen, Chao Gao and Zhao Ren, Robust Covariance and Scatter Matrix Estimation under Huber’s Contamination Model, §§1 and 5 (standard reference, not scraped)
- P. B. Stark, Statistics 240 Lecture Notes, Part 9: Robustness and Related Topics, §1.2, PDF pp. 10–12 (standard reference, not scraped)