On variance estimation under auxiliary value imputation in sample surveys
Bibliographic record
Abstract
We study the problem of variance estimation for a domain total when auxiliary value imputation, sometimes called cold-deck or substitution imputation, has been used to fill in missing data. We consider two approaches to inference which lead to different variance estimators. In the first approach, the validity of an impu- tation model is required. Our proposed variance estimator is nevertheless robust to misspecification of the second moment of the model. Under this approach, we show the somewhat counter-intuitive result that the total variance of the imputed estima- tor can be smaller than the sampling variance of the complete-data estimator. We also show that the na¨ ive variance estimator (i.e. the variance estimator obtained by treating the imputed values as observed values) is a consistent estimator of the total variance when the sampling fraction is negligible. In the second approach, the validity of an imputation model is not required but response probabilities need to be estimated. Our mean squared error estimator is obtained using robust estimates of response probabilities and is thus only weakly dependent on modeling assump- tions. We also show that both approaches lead to asymptotically equivalent total mean squared errors provided that the imputation model underlying the imputed estimator is correctly specified and the sampling fraction is negligible. Finally, we propose a hybrid variance estimator that can be viewed as a compromise between the two approaches. A simulation study illustrates the robustness of our proposed variance (mean squared error) estimators.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.081 | 0.243 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".