Download
a complete copy of this risk analysis resource for free here.
|
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.
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.
