# Jackknife Estimator: Simple Definition & Overview

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
,
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.