PRECISION ESTIMATION IN SAMPLE SURVEY INFERENCE - A CRITERION FOR CHOICE BETWEEN VARIANCE ESTIMATORS

We advocate the 'mean squared error of predicted squared error' as a universal criterion for the choice between variance estimators in sample survey inference. The predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample. This makes the new measure more satisfactory than the simpler mean squared error of the; variance estimator. The criterion turns out to be the same for design-based as for model-based inference, and may also be used for comparison between the design- and model-based theoretical variances. The theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature. These calculations are primarily made under a proportional regression model, but consideration is also paid to model robustness. Three of the six estimators are shown to be inferior to the three others, which are approximately equivalent.