DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How 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 modulus

Definition

For an experiment ${P_{θ} : θ \in Θ}$ with nonempty $Θ$ (Statistical experiments), choose a sigma-algebra $T$ on $Θ$ and take $(Θ, T)$ as the measurable action space (Measurable spaces and measurable sets). Take the target-first loss $L : Θ \times Θ \to [0, + \infty]$ from Loss functions and risk with that action space. For $0 \leq ϵ < 1$ , define

ω (ϵ, Θ) = \sup {L (θ_{1}, θ_{2}) : θ_{1}, θ_{2} \in Θ, ∥ P_{θ_{1}} - P_{θ_{2}} ∥_{T V} \leq ϵ / (1 - ϵ)} .

Set $ω (1, Θ) = \sup_{θ_{1}, θ_{2} \in Θ} L (θ_{1}, θ_{2})$ , allowing $+ \infty$ . Total variation is the event-supremum convention $\sup_{A} ∣ P (A) - Q (A) ∣$ from Total variation distance for probability laws, with no factor $1 / 2$ .

Depends on

Used by

Dependency tree · two levels

11 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, §5, Theorem 5.1 (standard reference, not scraped)
Philippe Rigollet, 18.S997: High-Dimensional Statistics, Lecture Notes, Chapter 5 (standard reference, not scraped)