Balanced repeated replication

If there are s strata, we would ideally take all 2s ways of choosing the half-stratum; but if s is large, this may be infeasible.

Let H be a Hadamard matrix of size s, and choose one row per half-sample.

The orthogonality of rows of H ensures that our choices are uncorrelated between half-samples.

Then our estimate for the sampling variance of the statistic is the average of (ai − a)2.

This is (at least in the ideal case) an unbiased estimate of the sampling variance.