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.

Lower empirical quantile of bootstrap values

Definition

Input a nonempty finite list $y_{1}, \dots, y_{B} \in R$ and $p \in [0, 1]$ . Sort the values with multiplicity as $y_{(1)} \leq \dots \leq y_{(B)}$ . If $p = 0$ , set $k = 1$ ; if $p > 0$ , let $k$ be the least integer in ${1, \dots, B}$ with $k \geq B p$ . Return $Q_{B} (p) = y_{(k)} .$ This is the lower inverse empirical-CDF quantile, with the explicit endpoint convention $Q_{B} (0) = y_{(1)}$ and $Q_{B} (1) = y_{(B)}$ . Repeated values remain repeated; no interpolation is performed. An empty list or a value of $p$ outside $[0, 1]$ is inadmissible.

Used by

Basic bootstrap interval Algorithm
Bias-corrected and accelerated bootstrap interval Algorithm
Bias-corrected bootstrap interval Algorithm
Bootstrap-t interval Algorithm
Percentile bootstrap interval Algorithm
Discrete median bootstrap with ties Example

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Bradley Efron and Robert Tibshirani, The Bootstrap Method for Assessing Statistical Accuracy, Behaviormetrika 12 (1985), §7 (standard reference, not scraped)