Adjusted Empirical Likelihood and its Properties
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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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 | 0.013 | 0.149 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".