Jackknife Resampling
Also known as: leave-one-out resampling, Quenouille-Tukey jackknife, delete-one jackknife, Jackknife Yeniden Örnekleme
The jackknife is a classical resampling method that estimates the bias and variance of a statistic by systematically recomputing it with one observation left out at a time. Introduced by Quenouille in 1956 and later reviewed by Miller in 1974, it predates the bootstrap and remains a simple, deterministic tool for assessing estimator stability.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the jackknife to estimate the bias or variance — and hence the standard error — of a statistic when no convenient closed-form formula exists, for both continuous and categorical data. It assumes the observations are independent, and the computational cost scales linearly with n. It needs at least about 10 observations to be reliable; for very small samples the bootstrap or a permutation test is preferred.
Strengths & limitations
- Simple and fully deterministic: the same data always give the same result, unlike the random bootstrap.
- Requires no closed-form variance formula, so it works for statistics whose sampling distribution is hard to derive analytically.
- Computational cost grows only linearly with the sample size n.
- Applies to both continuous and categorical data and to a wide range of summary statistics.
- Below about 10 observations the jackknife variance estimate becomes unreliable and the bootstrap should be used instead.
- With fewer than 5 observations leave-one-out resampling is essentially meaningless.
- It performs poorly for non-smooth statistics such as the median or sample quantiles, where the bootstrap is more appropriate.
- It assumes independent observations and offers no built-in correction for dependent or clustered data.
Frequently asked
How does the jackknife differ from the bootstrap?
The jackknife systematically leaves out one observation at a time, producing exactly n deterministic replicates, whereas the bootstrap draws many random samples with replacement. The jackknife is simpler and reproducible but less accurate for non-smooth statistics; the bootstrap is more flexible and is preferred for small samples and for statistics like the median.
How many observations do I need?
At least about 10. Below that the jackknife variance estimate is unreliable and the bootstrap is recommended; with fewer than 5 observations leave-one-out resampling is essentially meaningless and a permutation test is the better choice.
Why is there an (n-1)/n factor in the variance formula?
Leave-one-out estimates differ from the full-sample estimate by only a small amount, so their raw spread understates the true sampling variability. The (n-1)/n inflation factor rescales that spread to give a properly calibrated variance estimate.
Can the jackknife be used for any statistic?
It works well for smooth statistics such as means, ratios, and regression coefficients, but it performs poorly for non-smooth statistics like the median or sample quantiles, where the bootstrap is the safer alternative.
Sources
- Quenouille, M. H. (1956). Notes on Bias in Estimation. Biometrika, 43(3/4), 353-360. DOI: 10.1093/biomet/43.3-4.353 ↗
- Miller, R. G. (1974). The Jackknife — A Review. Biometrika, 61(1), 1-15. DOI: 10.1093/biomet/61.1.1 ↗
How to cite this page
ScholarGate. (2026, June 1). Jackknife Resampling. ScholarGate. https://scholargate.app/en/statistics/jackknife
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.
- Bootstrap InferenceStatistics↔ compare
- MAD EstimationStatistics↔ compare
- OLS RegressionEconometrics↔ compare
- Permutation TestStatistics↔ compare
- Robust Time Series AnalysisStatistics↔ compare