Estimation of design‐based mean squared error of a small area mean model‐based estimator under a nested error linear regression model
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Bibliographic record
Abstract
Abstract In this article, we propose a conditional model estimator (cmmse) for the design‐based mean squared error (dMSE) of a small area mean estimator under the basic unit level model. The mean squared error dMSE refers to the variability of a small area estimator over all possible sample selections. It is different from the model mean squared error (mMSE), traditionally used to measure the efficiency in small area estimation problems. For known model parameters, Rao, Rubin‐Bleuer & Estevao [Rao et al., Survey Methodology 2018; 44, 151–166] showed that dMSE depends on two quadratic finite population parameters. A design estimator of dMSE, denoted as dmse, is obtained by substituting the quadratic parameters with their corresponding design unbiased estimators. Rao, Rubin‐Bleuer & Estevao [Rao et al., Survey Methodology 2018; 44, 151–166] proposed a composite MSE estimator (cmse) based on both the design and the model. This estimator is defined as a weighted average between the design‐based dmse and a model‐based estimator (mmse). Given known variance components, we obtain a new formula for dMSE that accounts for the estimation of the fixed model coefficients. Our conditional model MSE estimator cmmse is obtained by replacing the quadratic finite population parameters by their best predictions under the model, in the new formula of dMSE. Properties of the proposed estimator are studied in terms of design bias, relative root mean squared error, coverage rate and a score function of the confidence intervals.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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