Rank theory approach to ridge, LASSO, preliminary test and Stein‐type estimators: A comparative study
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In the development of efficient predictive models, the key is to identify suitable predictors to establish a prediction model for a given linear or nonlinear model. This paper provides a comparative study of ridge regression, least absolute shrinkage and selector operator (LASSO), preliminary test (PTE) and Stein‐type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank‐based ridge estimator outperforms the usual rank estimator, restricted R‐estimator, rank‐based LASSO, PTE and Stein‐type R‐estimators uniformly. On the other hand, neither LASSO nor the usual R‐estimator, preliminary test and Stein‐type R‐estimators outperform the other. The region of dominance of LASSO over all the R‐estimators (except the ridge R‐estimator) is the sparsity‐dimensional interval around the origin of the parameter space. We observe that the L 2 ‐risk of the restricted R‐estimator equals the lower bound on the L 2 ‐risk of LASSO. Our conclusions are based on L 2 ‐risk analysis and relative L 2 ‐risk efficiencies with related tables and graphs. The Canadian Journal of Statistics 46: 690–704; 2018 © 2018 Société statistique du Canada
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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) | 0.000 | 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