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.

Bootstrap-t interval

Definition

Input an observed estimate $\hat{θ}$ , an observed standard error $\hat{s} > 0$ , and $B \geq 1$ pairs $({\hat{θ}}_{b}^{*}, {\hat{s}}_{b}^{*})$ with finite real ${\hat{θ}}_{b}^{*}$ and strictly positive finite ${\hat{s}}_{b}^{*}$ , produced from bootstrap samples under IID empirical bootstrap sample and mean statistic. If the observed or any bootstrap standard error is nonpositive or nonfinite, return undefined. Otherwise form $t_{b}^{*} = \frac{{\hat{θ}}_{b}^{*} - \hat{θ}}{{\hat{s}}_{b}^{*}}, b = 1, \dots, B .$ With $Q_{B}$ from Lower empirical quantile of bootstrap values and $p = α / 2$ for a supplied $0 < α < 1$ , return $[\hat{θ} - \hat{s} Q_{B} (1 - p), \hat{θ} - \hat{s} Q_{B} (p)] .$ The standard-error procedure is an explicit input; this algorithm alone establishes no studentized limit or coverage.

Depends on

Used by

Nothing in the library uses this result yet.

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)