Jackknife Empirical Likelihood Test for Equality of Two High Dimensional Means
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Bibliographic record
Abstract
There is a long history of testing the equality of two multivariate means. A popular test is the Hotelling T 2 , but in large dimensions it performs poorly due to the possible inconsistency of sample covariance estimation. Bai and Saranadasa (1996) and Chen and Qin (2010) proposed tests not involving the sample covari- ance, and derived asymptotic limits, which depend on whether the dimension is fixed or diverges, under a specific multivariate model. In this paper, we propose a jackknife empirical likelihood test that has a chi-square limit independent of the dimension. The conditions are much weaker than those needed in existing methods. A simulation study shows that the proposed new test has a very robust size across dimensions and has good power.
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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 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.003 | 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