Pseudo‐empirical Bayes estimation of small area means based on James–Stein estimation in linear regression models with functional measurement error
Bibliographic record
Abstract
Abstract Small area estimation plays an important role in making reliable inference for subpopulations (areas) for which relatively small samples or no samples are available. In model‐based small area estimation studies, linear and generalized linear mixed models have been used extensively assuming that covariates are not subjected to measurement errors. Recently, there have been studies considering this problem under the functional measurement error for covariates using the maximum likelihood method and the method of moments. In this paper, we study the James–Stein estimator of the true covariate subject to the functional measurement error. To this end, we obtain a new pseudo‐empirical Bayes (PEB) predictor of small area means based on the James–Stein estimator. Then, we show that the new PEB predictor is asymptotically optimal. The weighted and unweighted jackknife estimators of the mean squared prediction error of the new PEB predictor are also derived. Simulation studies are conducted to evaluate the performance of the proposed approach. We observe that the PEB predictor based on the James–Stein estimator performs better than those based on the maximum likelihood method and the method of moments. Finally, we apply the proposed methodology to a real dataset. The Canadian Journal of Statistics 43: 265–287; 2015 © 2015 Statistical Society of Canada
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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 | 0.021 | 0.097 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".