An explicit multiple case-deletion formula for a linear regression model with correlated errors and a resulting property of the BLUP of a multivariate predictand
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Bibliographic record
Abstract
With reference to a linear model with correlated errors, we obtain an updation formula for the best linear unbiased estimator (BLUE) of the regression coefficients under multiple case-deletion. The generality and clarity of this formula, compared to its existing counterparts, facilitate its use. Specifically, the established formula leads to an attractive property of the best linear unbiased predictor (BLUP) of a multivariate predictand in terms of the invariance of the aforementioned BLUE as well as the residual sum of squares when the BLUP is substituted for actual observations. This property is illustrated with a numerical example on order statistics from a location-scale model.
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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 | 0.004 |
| 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 | 0.000 |
| 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