bootstrap instrument
| Definition | An 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. |
|---|---|
| Example | Resample 100 rows with replacement 1000 times, and the spread of the 1000 means is the bootstrap standard error. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id bootstrap, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
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| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Bootstrap.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- 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.
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.