Jack-Knife Resampling/Examples

Examples of Jack-Knife Resampling

Arbitrary Example

Let us attempt to determine the bias in the correlation coefficient $r$ of a sample of $n$ pairs used as an estimator of the correlation coefficient $\rho$ of the population.

The procedure is to compute successively the values $r_{\paren i}$ for $i = 1, 2, \ldots, n$ for sample identical to the original but with the $i$th sample value omitted.

Let $r_{\paren .}$ be the mean of the $r_{\paren i}$ values.

Then the jack-knife estimator of bias is given by:

$B = \paren {n - 1} \paren {r_{\paren .} - r}$

In general, this is not an exact measure of bias, but it is usually a good approximation.

Standard Errors

Jack-knifing can be used to obtain estimates of standard errors.

While the jack-knife involves only $n$ samplings of the original data, each of a specified form, the bootstrapping method often uses $N$ samplings, where $N$ is considerably greater than $n$.