On the arbitrariness of some asymptotic test statistics based on generalized inverses
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Under appropriate conditions, some asymptotic test statistics based on generalized inverses (g‐inverses) are shown to be arbitrary in the sense that any desired numerical value for a statistic can be obtained by appropriately choosing a g‐inverse of an estimator. Examples of statistics based on g‐inverses include score‐type and Hausman‐type statistics. Some versions of these statistics considered in the literature can be viewed as polar cases in the sense that their weighting matrices have either minimum or maximum rank. By associating a statistic with an estimator of a variance‐covariance matrix and by appropriately choosing the estimator, it is possible to construct a statistic that is invariant with respect to the choice of a g‐inverse of the estimator.
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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 | 0.008 |
| 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) | 0.002 | 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