Why BRR Works: Deep Dive Into Hadamard Matrix
Source: https://mathworld.wolfram.com/HadamardMatrix.html Going Deeper: The Mathematical Engine Behind BRR In our previous posts on Balanced Repeated Replication (BRR) and Fay’s method, we explored how these techniques solve the variance estimation problem in complex surveys. We saw the elegant result: create a set of replicate weights, recompute your statistics using each replicate, and combine the results to get variance estimates that properly account for the survey design. But we left something crucial as a black box: how exactly are these replicates constructed? We said “use a Hadamard matrix” and moved on, focusing instead on the weighting schemes and the variance formulas. For many practitioners, that’s sufficient – major survey data providers like the Medicare Current Beneficiary Survey (MCBS), NHANES, and many state-level behavioral health surveys provide pre-computed replicate weights in their public use files. You load the data, use the supplied weights, trust the mathematics, get your standard errors. ...