Unit level small area estimation with copulas
Bibliographic record
Abstract
Abstract The goal of this article is to predict the mean values of a survey variable Y in small areas using simple random samples of units drawn in these areas and known auxiliary variables x. Predictions obtained with non‐normal error distributions are investigated. Exchangeable models for the dependency between the regression errors within a small area are first proposed and the best unbiased predictors (BUPs) for unobserved Y, under the proposed models, are derived. They are compared to the best linear unbiased predictors (BLUPs). The second part of the article focuses on a particular class of models for Y, constructed using multivariate exchangeable copulas. They involve a regression parameter , a dependency parameter for the copula, , and , the marginal cumulative distribution function of the regression errors, considered as an infinite‐dimensional parameter. Semi‐parametric methods for estimating the parameters are proposed and small area predictions are constructed using these estimators. Conditional mean squared prediction error estimators, which account for the estimation of the parameters, are discussed. Copula selection is done using cross‐validation. This new methodology is illustrated through simulations and the analysis of a real data set. The Canadian Journal of Statistics 44: 397–415; 2016 © 2016 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 | 0.006 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".