Replication variance estimation after sample-based calibration
Section 5. Conclusions
We have proposed an approach to account for sample-based calibration in the variance estimates. The approach applies to situations in which both the survey being calibrated and the survey providing the calibration controls use replicate variance estimation, as is often the case in large-scale government surveys. The replication methods in each are arbitrary, as long as they are both valid for their specific surveys. We described the approach for the cases of calibration by regression estimation (including post-stratification) and raking, two commonly used methods in practice, and we anticipate it would work similarly for other types, such as the general calibration estimators of Deville and Särndal (1992).
The main alternative to the proposed method is that of Fuller (1998). Relative to that method, an important advantage of our approach is that it does not require computation of the estimated variance-covariance matrix of the control totals, so that it is very straightforward to implement. In the typical application in which the number of control totals is smaller than the number of replicates, another potential advantage of the proposed method is that the perturbations will be applied across a larger fraction of the replicates. This reduces the risk of computing replicate variance estimates that do not fully reflect the variability of the control totals. For instance, this can occur when only a subset of the replicates contributes to the variance estimate of a domain mean. If these replicates are mostly unperturbed, the resulting variance estimate can underestimate the variance. Further investigation of the performance of the proposed method when the number of replicates of the two surveys are different appears warranted.
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