Adjusted Empirical Likelihood and its Properties
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Computing a profile empirical likelihood function, which involves constrained maximization, is a key step in applications of empirical likelihood. However, in some situations, the required numerical problem has no solution. In this case, the convention is to assign a zero value to the profile empirical likelihood. This strategy has at least two limitations. First, it is numerically difficult to determine that there is no solution; second, no information is provided on the relative plausibility of the parameter values where the likelihood is set to zero. In this article, we propose a novel adjustment to the empirical likelihood that retains all the optimality properties, and guarantees a sensible value of the likelihood at any parameter value. Coupled with this adjustment, we introduce an iterative algorithm that is guaranteed to converge. Our simulation indicates that the adjusted empirical likelihood is much faster to compute than the profile empirical likelihood. The confidence regions constructed via the adjusted empirical likelihood are found to have coverage probabilities closer to the nominal levels without employing complex procedures such as Bartlett correction or bootstrap calibration. The method is also shown empirical likelihood.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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