Statistics How To

Jackknife Estimator: Simple Definition & Overview

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The jackknife (“leave one out”) can be used to reduce bias and estimate standard errors. It is an alternative to the bootstrap method.

Comparison to Bootstrap

Like the bootstrap, the Jackknife involves resampling. The main differences are:

Overview of the Jackknife Procedure

The basic idea is to calculate the estimator (e.g. the sample mean) by sequentially deleting a single observation from the sample. The estimator is recomputed until there are n estimates for a sample size of n. As a simple example, let’s say you had five data points X1, X2, X3, X4, X5. You would calculate the estimator five times, for:

  • X1, X2, X3, X4, X5.
  • X2, X3, X4, X5.
  • X3, X4, X5.
  • X4, X5.
  • X5.

Once you have your n estimates
jackknife estimates,
the standard error is calculated with the following formula:

Why Use Jackknife Estimation?

Jackknife estimation is usually used when it’s difficult or impossible to get estimators using another method. For example:

  • No theoretical basis is available for estimation,
  • The statistics’s function is challenging to work with (e.g. a function with no closed form integral, which would make the usual method (the delta method) impossible),

For large samples, the Jackknife method is roughly equivalent to the delta method.

References

The Bootstrap and Jack knife. Retrieved November 2, 2019 from: https://www.biostat.washington.edu/sites/default/files/modules/2017_sisg_1_9_v3.pdf
McIntosh, A. The Jack knife Estimation Method. Retrieved November 2, 2019 from: http://people.bu.edu/aimcinto/jackknife.pdf
Ramachandran, K. & Tsokos, C. (2014). Mathematical Statistics with Applications in R. Elsevier.

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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