Some Comments on the Watson Efficiency of the Ordinary Least Squares Estimator Under the Gauss Markov Model
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Bibliographic record
Abstract
We consider the estimation of a given estimable parametric function in the Gauss–Markov model, and focus on questions concerning the Watson efficiency of the ordinary least squares estimator (OLSE) of the given parametric function with respect to the best linear unbiased estimator (BLUE). We apply the Frisch–Waugh–Lovell Theorem for the estimation of the parametric function, and give an interesting decomposition of the total Watson efficiency with respect to the efficiency of the parametric function. Also, a relation between the Watson efficiency of the OLSE of the given parametric function and specific canonical correlations is established.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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