Empirical likelihood tests for two-sample problems via nonparametric density estimation
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Bibliographic record
Abstract
The authors study the problem of testing whether two populations have the same law by comparing kernel estimators of the two density functions. The proposed test statistic is based on a local empirical likelihood approach. They obtain the asymptotic distribution of the test statistic and propose a bootstrap approximation to calibrate the test. A simulation study is carried out in which the proposed method is compared with two competitors, and a procedure to select the bandwidth parameter is studied. The proposed test can be extended to more than two samples and to multivariate distributions. Tests de vraisernblance ernpirique pour deux populations deduits d'estirnations non parametriques de leurs densites Les auteurs s'intéressent au problème de tester l'égalité des lois de deux populations, en comparant des estimateurs à noyaux de leurs densités. La statistique de test proposée est basée sur une approche de vraisemblance empirique locale. La distribution asymptotique de la statistique du test est obtenue et une approximation par bootstrap est proposée aux fins de calibration. Une étude de simulation est effectuée, dans laquelle la méthode proposée est comparée avec deux compétiteurs et une procédure de sélection du paramètre de lissage est étudiée. Le test proposé peut ětre généralisé à plus de deux échantillons et au cas de distributions multivariées.
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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 | 0.001 |
| 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