On the Distributions of some Test Statistics for Profile Analysis in Elliptical Populations
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Bibliographic record
Abstract
SYNOPTIC ABSTRACTThe upper percentiles for the distributions of the test statistics in profile analysis are discussed. These test statistics are Hotelling's T2-type statistic in normal populations and their upper percentiles are expressed by that of the F-distributions. In elliptical populations, however, it is difficult to express them exactly. Then asymptotic expansions for the distributions of the test statistics are derived by the perturbation method and we obtain approximate upper percentiles for the distributions of the test statistics. The effect of nonnormality on approximations is discussed and the approximate accuracy is evaluated via a Monte Carlo simulation study.Key Words and Phrases: asymptotic expansionHotelling's T2-statisticnon-normalityMonte Carlo simulation
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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