Empirical likelihood tests for two-sample problems via nonparametric density estimation
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.
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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 | 0.033 | 0.235 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".