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Also known as: Leave-One-Out Resampling
Resampling method estimating bias and variance by systematically leaving out each observation and recomputing the statistic.
DESCRIPTION
The jackknife forms n leave-one-out datasets from a sample of size n to assess estimator variability and bias. It produces pseudovalues and simple variance estimates with low computational cost. Historically predating bootstrap, it’s useful for smooth statistics and identifying influential observations. Jackknife can fail for non-smooth statistics (e.g., medians) where bootstrap performs better. It’s a staple in nonparametric inference and model diagnostics.
ALTERNATIVE DEFINITIONS
Wikipedia
The jackknife resampling technique estimates the bias and variance of a statistic by systematically leaving out each observation from a dataset and calculating the statistic over the remaining observations.
Defines the leave-one-out procedure and focus on bias/variance estimation.
NIST
The jackknife is a technique for estimating the bias and variance of a statistic by deleting one observation at a time from the data set and recomputing the statistic.
Concise operational definition from a standards body.
StatLect
The jackknife estimates the variability of a statistic by constructing leave-one-out subsamples and combining the resulting values.
Highlights construction of subsamples and combining estimates.
RELATED TERMS
Leave-One-Out Systematic Error Variance Pseudovalue Estimator Confidence Interval Cross-Validation Nonparametric Methods Resampling
COMPETING TERMS
KNOWLEDGE AREAS
TARGET AUDIENCE
EXTERNAL SOURCES
- Wikipedia - Jackknife resampling
- NIST - NIST handbook section on jackknife
- StatLect - Jackknife tutorial and examples
- Wolfram MathWorld - Definition and properties
TOP QUESTIONS
What is the Jackknife method?
It’s leave-one-out resampling to estimate bias and variance by recomputing a statistic without each observation in turn.
Category: Definition
Why use Jackknife over Bootstrap?
Jackknife is simpler and less computationally intensive. It performs well for smooth statistics but may be less accurate than bootstrap for non-smooth ones.
Category: Alternatives
What are pseudovalues in Jackknife?
They’re transformed leave-one-out estimates used to compute variance and bias conveniently.
Category: Definition
What mistakes occur with Jackknife?
Applying it to non-smooth statistics or small samples can lead to poor estimates. Ignoring influential points skews results.
Category: Mistakes
How many resamples does Jackknife use?
Exactly n for a sample of size n, each omitting one observation.
Category: Requirements
Can Jackknife handle dependence?
For time series, block jackknife variants may be needed; naive leave-one-out breaks temporal structure.
Category: Application
Who pioneered the Jackknife?
It was developed by Maurice Quenouille and later expanded by John Tukey, predating bootstrap.
Category: Origin
How does Jackknife help diagnostics?
It reveals influential observations by examining changes in the statistic when each point is removed.
Category: Example
What is a competing method to Jackknife?
Bootstrap resampling generally provides more flexible and accurate uncertainty quantification at higher computational cost.
Category: Alternatives