Improved Estimation of Coefficient Vector in a Regression Model
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Bibliographic record
Abstract
Abstract In this article we consider the problem of estimating the coefficient vector of a classical regression model when it is apriori suspected that the parameters vector may belong to a subspace. Two estimators; namely the positive-part of Stein-type estimator and the improved preliminary test estimator are proposed and it is demonstrated analytically as well as numerically that the proposed estimators dominate the usual Stein-type and pretest estimators respectively. The proposed estimators are also compared in terms of risks with that of the unrestricted estimator and we find that the positive-part of Stein-type estimator uniformly dominates the unrestricted estimator while the improved preliminary test estimator dominates the unrestricted estimator in a wider range than that of the usual pretest estimator. Keywords: Uncertain prior informationQuadratic biasesMean squared error matricesRisk functionsImproved pretest estimatorPositive-part of James–Stein estimatorPercentage risk improvement Acknowledgment The authors are thankful to the referee for helpful comments on the earlier draft.
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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 | 0.000 | 0.001 |
| 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