One of the earliest techniques to obtain reliable statistical estimators is the jackknife technique. It requires less computational power than more recent techniques.
Suppose we have a sample and an estimator
. The jackknife focuses on the samples that leaves out one observation at a time:
The jackknife estimate of s.e. defined by
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(3) |
The jackknife only works well for linear statistics (e.g., mean). It fails to give accurate estimation for non-smooth (e.g., median) and nonlinear (e.g., correlation coefficient) cases. Thus improvements to this technique were developed.