The Jackknife

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See also: The Bootstrap, Analyzing and using data introduction, The parametric Bootstrap, The non-parametric Bootstrap, VoseNBoot,

The Bootstrap was originally developed from a much earlier technique called the Jackknife, invented by the brilliant and practical statistician John Wilder Tukey (1915-2000). The Jackknife was used to review the robustness of a statistic calculated from a set of data. A Jackknife value was the statistic of interest calculated with the ith value removed from the data set and is given the notation . With a data set of n values, one thus has n Jackknife values, the distribution of which gives a feel for the uncertainty one has about the true value of the statistic. We say 'gives a feel' because the reader is certainly not recommended to use the Jackknife as a method for obtaining any precise estimate of uncertainty. The Jackknife turns out to be an awful estimation of uncertainty.

Example:

This example model performs a Jackknife analysis on a data set in an attempt to evaluate the uncertainty about the population's mean and standard deviation. A non-parametric Bootstrap is performed on the same data set, and the results of the two techniques are shown below. The Jackknife clearly provides a distribution with far too little spread.

 

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