Multivariate local polynomial regression for estimating average derivatives
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Bibliographic record
Abstract
In this paper we suggest to use the sample average of the derivative estimators from a local polynomial fitting to estimate the average derivatives of an unknown multivariate function. Using the techniques of Masry (1996a Masry, E. (1996a). Multivariate regression estimation local polynomial fitting for time series. Stochastic Processes and Their Applications, 65: 81–101. [Crossref], [Web of Science ®] , [Google Scholar],b) Masry, E. (1996b). Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis, 17: 571–599. [Crossref] , [Google Scholar], we derive the asymptotic normal distribution of the proposed average derivative estimator. Monte Carlo experiments show that the proposed estimator compares well with the existing estimators.
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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 | 0.043 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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