Jack-Knife Resampling/Examples/Arbitrary Example 1
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Example of Jack-Knife Resampling
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.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): jack-knife