Balanced repeated replication half-samples

Builds replicate weights from a Hadamard matrix, one PSU per stratum in each half-sample.

Usage

morie_brr_balanced(strata, fay_k = 0)

Arguments

strata

stratum label per PSU; every stratum needs exactly 2.

fay_k

Fay factor in [0, 1).

Value

list with replicate_weights (R x n), n_replicates, hadamard, n_strata.

Details

The Hadamard orthogonality is the whole trick: it is why R replicates of order H suffice where the \(2^H\) possible half-samples would not be enumerable. Using fewer replicates than strata destroys the balance and biases the variance downward.

Fay's adjustment replaces the 0/2 weights with k and 2-k, which keeps every unit in every replicate – necessary when a zero weight would make a domain empty. It must be paired with the \((1-k)^2\) divisor in morie_brr_variance.

References

Wolter, K. M. (2007). Introduction to Variance Estimation, 2nd ed., Ch. 3. Springer. Judkins, D. R. (1990). Fay's method for variance estimation. JOS, 6(3), 223-239.

Examples

morie_brr_balanced(rep(1:4, each = 2))$n_replicates
#> [1] 4