Performance of Positive Rule Estimator in the Ill-Conditioned Gaussian Regression Model
Why this work is in the frame
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Bibliographic record
Abstract
Ridge regression is a widely used method to estimate the regression parameters for an ill-conditioned model. This paper describes the estimation of the regression parameters for the Gaussian linear regression model with ill-conditioned explanatory variables. We propose some improved estimators, namely, the unrestricted ridge regression estimator, restricted ridge regression estimator, preliminary test ridge regression estimator, shrinkage ridge regression estimator and positive rule ridge regression estimators in this paper. The performances of the proposed estimators are compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for departure and ridge parameters are given. It is demonstrated that unlike the positive rule shrinkage (PR) estimator which dominates both unrestricted and shrinkage estimators, the positive rule ridge regression estimator (PRRRE) utilizes both sample and non-sample information but does not outperform the unrestricted and shrinkage ridge regression estimators for an ill-conditioned data. Some graphical representations have been presented which support the findings of the 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 | 0.001 | 0.006 |
| 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