Bootstrap Inference
Bootstrap Resampling Inference · Also known as: bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı
Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.
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When to use it
Use the bootstrap when you need a confidence interval or standard error for a statistic but cannot rely on a normality or large-sample assumption — for example with skewed data, small samples, or a statistic with no simple closed-form variance. It applies to continuous, categorical, and ordinal data and to most study structures. Two conditions matter: observations should be independent, and the original sample must be representative of the population. At least about 10 observations are needed, and results grow shaky below 20.
Strengths & limitations
- Distribution-free: it needs no normality assumption and works for statistics that lack a tractable variance formula.
- Provides reliable confidence intervals in small samples where classical large-sample approximations fail.
- Conceptually simple and broadly applicable across continuous, categorical, and ordinal data and many statistics.
- With very small samples (n < 20) the resampling diversity is too limited and the confidence intervals become unreliable.
- Below about 10 observations the bootstrap distribution is essentially meaningless, and an exact test should be preferred.
- It assumes independent observations and a representative original sample; if the sample is biased or dependent, the bootstrap faithfully reproduces that bias.
Frequently asked
What is the difference between the bootstrap and the jackknife?
The jackknife systematically leaves out one observation at a time, while the bootstrap resamples with replacement to build a full empirical sampling distribution. The bootstrap is more general and usually more accurate, but for extremely small samples (under 10) the jackknife or an exact test is the safer choice.
How many bootstrap resamples should I use?
For confidence intervals, at least about 1000 resamples are recommended so the percentile estimates settle down; more is better when computation allows. Too few resamples leave the interval noisy and unstable.
Does the bootstrap fix a biased sample?
No. The bootstrap only reproduces the information already in your sample. If the original sample is non-representative or the observations are dependent, the method will faithfully carry that bias into the confidence interval.
When should I prefer a permutation test instead?
When the sample is very small (below about 20) the bootstrap's resampling diversity is too limited; a permutation test, which derives the distribution from rearrangements of the data, is then more reliable for comparison-type questions.
Sources
- Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26. DOI: 10.1214/aos/1176344552 ↗
- Efron, B. & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC Press. ISBN: 978-0412042317
How to cite this page
ScholarGate. (2026, June 1). Bootstrap Resampling Inference. ScholarGate. https://scholargate.app/en/statistics/bootstrap-inference
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- JackknifeStatistics↔ compare
- Permutation TestStatistics↔ compare
- Robust CorrelationStatistics↔ compare
- Trimmed Mean TestStatistics↔ compare
- Winsorized EstimationStatistics↔ compare