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There is a simple motivation to use re-sampling methods. In fact let us consider a set of independent and identically distributed data samples
of an unknown probability distribution
We can compute the sample average
, and then we can estimate the accuracy of
using the standard deviation:
The trouble with this formula is that it does not, in any obvious way, extend to estimators other than
. For this reason a generalized version of A.2 is introduced such that it reduces to the usual standard deviation when the chosen estimator is the average.