Intermediary between the complete enumeration of all samples and the drawing of a few samples at random lies the Balanced Bootstrap, (see Gleason, 1988, American Statistician,263-266) for a simple algorithm.

The idea is that as when we count all samples each observation has the same chance of appearing, we would like to have each observation appearing overall the same number of times after all bootstrap resamples have been drawn.

We can be ensured of this by taking a list of repetitions of each of the observations and repeating them times, take a permutation of these values and then take the first as the first sample, and so on.

Susan Holmes 2004-05-19