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.

Risk domination and admissibility

Definition

For two decision rules $δ_{0}, δ_{1}$ in one decision problem, $δ_{1}$ dominates $δ_{0}$ if $R (θ, δ_{1}) \leq R (θ, δ_{0})$ for every parameter $θ$ , with strict inequality for at least one $θ$ . A rule is admissible if no decision rule dominates it; otherwise it is inadmissible. Risk is the extended-valued function of Loss functions and risk. Admissibility is a pointwise comparison across the whole parameter set; it does not assert that the rule minimizes risk at any particular parameter or under a global criterion.

Depends on

Loss functions and risk

Used by

A data-dependent rule dominates a constant rule Example

Dependency tree · two levels

6 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

Ryan Martin, Lecture Notes on Advanced Statistical Theory, §5.2, PDF pp. 102–104 (standard reference, not scraped)
Peter Hoff, Statistical Decision Problems, §5, PDF pp. 11–12 (standard reference, not scraped)