How jackknifing works
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The jackknife method uses less computational effort than a bootstrap analysis and is thus often quicker and easier to undertake. However, it cannot be used to estimate confidence intervals.
The general scheme is as follows:
1. Consider a situation where a parameter is to be estimated from n samples, e.g. a species diversity index from 10 kicknet samples from a stream.
2. Use all n samples to calculate the parameter of interest, E, the diversity index.
3. Now remove one of the samples at a time and recalculate the parameter of interest, Ei.
4. Calculate the pseudovalues for the parameter of interest :
where n = the total number of replicates, E = the estimate for all n samples, Ei = the estimate with sample i removed.
5. Estimate the mean and standard error of the parameter of interest from the n pseudovalues. The jackknife estimate of bias is E - the mean of the pseudovalues and the estimate of the standard error of the sample is simply the standard error of the pseudovalues:
is the mean of the pseudovalues.