On the Expressions of Estimability in Testing General Linear Hypotheses
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Bibliographic record
Abstract
Abstract In testing a general linear hypothesis of the form K ′β ∊ ( W ′) under a general linear model, an equivalent hypothesis involving only estimable parametric functions is provided, and then an explicit test statistic in terms of the model matrices is given. The corresponding results are expanded to the case of a general linear model with a restriction and are illustrated by an example. Keywords: Equivalent general linear hypothesesEstimabilityEstimable functionsGeneral linear modelsTestable hypothesisMathematics Subject Classification: Primary 62F03Secondary 62H15 Acknowledgments The authors are grateful to the referee and to the editor for their very helpful suggestions, which led to the improved version of this paper.
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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 | 0.006 | 0.061 |
| 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 | 0.001 |
| 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