Efficient Estimation of Quadratic Finite Population Functions in the Presence of Auxiliary Information
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Bibliographic record
Abstract
By viewing quadratic and other second-order finite population functions as totals or means over a derived synthetic finite population, we show that the recently proposed model calibration and pseudoempirical likelihood methods for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second-order finite population functions. In particular, estimation of a finite population variance, covariance, or variance of a linear estimator can be greatly improved when auxiliary information is available. The proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct. They have a number of attractive features, which include applicability to a general sampling design, incorporation of information on possibly multivariate auxiliary variables, and the ability to entertain linear or nonlinear working models, and they result in nonnegative estimates for certain strictly positive quantities such as variances. Several existing estimators are shown to be special cases of the proposed general methodology under a linear working model.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.016 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it