AlgorithmAlgorithm: 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.

Basic bootstrap interval

Definition

Input the observed estimate $\hat{θ}$ , a nonempty list of $B$ bootstrap estimates ${\hat{θ}}_{1}^{*}, \dots, {\hat{θ}}_{B}^{*}$ generated under IID empirical bootstrap sample and mean statistic, and $0 < α < 1$ . Let $Q_{B}$ be Lower empirical quantile of bootstrap values and set $p = α / 2$ . Return $[2 \hat{θ} - Q_{B} (1 - p), 2 \hat{θ} - Q_{B} (p)] .$ This is the reflected bootstrap-quantile interval under the declared finite-sample quantile convention. It makes no coverage claim.

Depends on

Used by

Discrete median bootstrap with ties Example

Dependency tree · two levels

13 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

Bradley Efron and Robert Tibshirani, The Bootstrap Method for Assessing Statistical Accuracy, Behaviormetrika 12 (1985), §§4 and 7 (standard reference, not scraped)
A. C. Davison and D. V. Hinkley, Bootstrap Methods and Their Application, Chapter 5, §5.2, Basic Confidence Limit Methods (standard reference, not scraped)