Shrinkage estimation and selection for a logistic regression model
Why this work is in the frame
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Bibliographic record
Abstract
This paper considers the problem of variable selection and the esti- mation for a logistic regression model via shrinkage and three penalty methods. We develop a large sample theory for the shrinkage estimators including as- ymptotic distributional bias and risk. We show that if the shrinkage dimension exceeds two, the asymptotic risk of the shrinkage estimator is strictly less than the classical estimators for a wide class of models. This reduction holds glob- ally in the parameter space. Furthermore, we consider three different penalty estimators: the LASSO, adaptive LASSO, and SCAD and compare their rel- ative performance with the shrinkage estimators numerically. A Monte Carlo simulation study is conducted for different combinations of inactive predictors and the performance of each method is evaluated in terms of a simulated mean squared error. This study indicates that shrinkage method is comparable to the LASSO, adaptive LASSO, and SCAD when the number of inactive pre- dictors in the model is relatively large. A real data example is presented to illustrate the proposed methodologies.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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