To form the exhaustive bootstrap distribution of a statistic one need only compute each of the statistics and associate a weight with it. The shift from to C n gives substantial savings. For the law school data, while . Efficient updating avoids multiplying such large numbers by factors of n . This is what makes the computation feasible.
Gray codes generate compositions by changing two coordinates of the vector by one up and one down.
This means that can be easily updated by multiplying and dividing by the new coordinates. Similar procedures, discussed in Section C below allow efficient changes in the statistics of interest. Gray codes for compositions. These four lists are then concatenated by writing the first, the second in reverse order, the third in its original order followed by the fourth in reverse order. The lists generated in this way have the property that two successive compositions differ only by in two coordinates.