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.

Regular estimator under local alternatives

Definition

In a local experiment ${P_{n, h} : h \in R^{d}}$ at $h = 0$ (Local asymptotic normality for local experiments), let $T_{n}$ be an $R^{d}$ -valued statistic. It is regular at zero with limit law $W$ if, for every fixed $h \in R^{d}$ , $T_{n} - h \Rightarrow W under P_{n, h},$ where the same probability law $W$ works for all $h$ . In a parametric model with true parameter $θ_{0}$ , this is the definition for $T_{n} = \sqrt{n} ({\hat{θ}}_{n} - θ_{0})$ and local laws at $θ_{0} + h / \sqrt{n}$ ; equivalently the centered error $\sqrt{n} ({\hat{θ}}_{n} - θ_{0} - h / \sqrt{n})$ has a limit independent of the fixed local displacement $h$ .

Depends on

Used by

Dependency tree · two levels

7 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

Peter Bartlett, Theoretical Statistics, Stat 210B Lecture 21, PDF pp. 19–22 (standard reference, not scraped)
John Duchi, A few notes on contiguity, asymptotics, and local asymptotic normality, §4 (standard reference, not scraped)