Rank theory approach to ridge, LASSO, preliminary test and Stein‐type estimators: A comparative study
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 L2‐risk of the restricted R‐estimator equals the lower bound on the L2‐risk of LASSO. Our conclusions are based on L2‐risk analysis and relative L2‐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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.037 | 0.093 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".