Poisson Sampling, Regression Estimation, and the Delete-a-Group Jackknife
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When coupled with the simple expansion estimator, Poisson sampling leads
to estimators with higher-than-necessary variances. That problem vanishes
when the expansion estimator is replaced by a randomization-consistent
regression estimator. A simultaneous estimator for the model variance and
randomization mean squared error of this estimation strategy is developed.
It is nearly identical to the weighted residual variance estimator, but can be
slightly better at estimated the model variance when finite population
correction matters. When finite population correction can be ignored, an
appropriately-defined delete-a-group jackknife variance estimator is shown
to have desirable asymptotic properties making it a practical alternative in
many applications.