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.

Gross-error contamination path

Definition

For probability measures $F, H$ on a common measurable space $(X, A)$ (Probability measures and probability spaces) and $0 \leq ϵ \leq 1$ , the gross-error path is $F_{ϵ, H} = (1 - ϵ) F + ϵ H$ , a probability measure by A convex mixture of probability laws is a probability law. For any $x \in X$ , its point-contamination direction at $x$ is the specialization $H = δ_{x}$ (The Dirac set function at a point, A Dirac set function is a probability measure). The path is used for a derivative at $ϵ = 0$ ; the definition alone gives no uniform-in- $H$ remainder.

Depends on

Used by

Bounded influence can coexist with vanishing replacement breakdown Counterexample
Contamination-robust expected risk and tail risk Definition
Statistical functionals and gross-error influence functions Definition
The mean has an unbounded directional derivative supremum Example
Influence function and sensitivity of the median Theorem
Influence function for a regular M-location functional Theorem

Dependency tree · two levels

8 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

P. B. Stark, Statistics 240 Lecture Notes, Part 9: Robustness and Related Topics, §1.2, PDF pp. 10–12 (standard reference, not scraped)
Mengjie Chen, Chao Gao and Zhao Ren, Robust Covariance and Scatter Matrix Estimation under Huber’s Contamination Model, §1 (standard reference, not scraped)