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bootstrap instrument

DefinitionAn estimate of a confidence interval made by resampling the data with replacement many times and recomputing the statistic each time. A paired bootstrap resamples the same rows for two methods at once so that shared sampling variation cancels. Chapter 0 section 0.9.
ExampleResample 100 rows with replacement 1000 times, and the spread of the 1000 means is the bootstrap standard error.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id bootstrap, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • An interval estimated by resampling the data with replacement and recomputing the statistic each time. A paired bootstrap resamples the same rows for two methods at once, and the variance of the difference is the sum of the two variances minus twice their covariance, so pairing narrows the interval exactly when the two scores covary positively across rows.
  • Resampling rows does not undo dependence between folds, which is the correction’s job, and the bootstrap’s interval is only as wide as the sample it resamples.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/Bootstrap.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
00.51estimateresamples of the same rows
Resampling the rows with replacement to see how far the estimate moves.

Equation

none

Conditions

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Efron, bootstrap methods, 1979, as chapter 0 section 0.9 states it, with the program’s paired form in the flip comparisons of Volume 14 and the constraint-gap review.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Bootstrap.lean, theorems mean_sub, var_sub, paired_lt_iff, cov_comm, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer S, chapters 0, 6, 7, 11, 12, 14.

Related

confidence interval; standard error; Nadeau and Bengio correction; harness.

See also

Book equations stated beside the entry’s terms, not defining it: 8.2, 0.18.

Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.4, chapter 8 section 8.5.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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