Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models
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Bibliographic record
Abstract
Empirical Bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data. However, estimation of the unconditional mean squared error of prediction is complicated, particularly for a nonlinear mixed model. Jiang et al. (2002) proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting estimator is nearly unbiased. The leading term of this estimator does not depend on the area-specific responses in the nonlinear case, whereas the posterior variance of the small area parameter given the model parameters is area-specific. Rao (2003) proposed an alternative method that leads to a computationally simpler jackknife estimator with an area-specific leading term. We show that a modification of Rao's method leads to a nearly unbiased area-specific jackknife estimator, which is also nearly unbiased for the conditional mean squared error given the area-specific responses. We examine the relative performances of the jackknife estimators, conditionally as well as unconditionally, in a simulation study, and apply the proposed method to estimate small area mean squared errors in disease mapping problems.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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