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.

Percentile bootstrap interval

Definition

Input a nonempty list of $B$ bootstrap estimates ${\hat{θ}}_{1}^{*}, \dots, {\hat{θ}}_{B}^{*}$ generated under the empirical bootstrap law in 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 $[Q_{B} (p), Q_{B} (1 - p)] .$ This finite- $B$ procedure uses the declared lower empirical-quantile convention. It defines endpoints only; it asserts no coverage guarantee.

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), §7 (standard reference, not scraped)