Penalized high‐dimensional M‐quantile regression: From <i>L</i><sup>1</sup> to <i>L</i><sup><i>p</i></sup> optimization
Bibliographic record
Abstract
Abstract Quantiles and expectiles have been receiving much attention in many areas such as economics, ecology, and finance. By means of L p optimization, both quantiles and expectiles can be embedded in a more general class of M‐quantiles. Inspired by this point of view, we propose a generalized regression called L p ‐quantile regression to study the whole conditional distribution of a response variable given predictors in a heterogeneous regression setting. In this article, we focus on the variable selection aspect of high‐dimensional penalized L p ‐quantile regression, which provides a flexible application and makes a complement to penalized quantile and expectile regressions. This generalized penalized L p ‐quantile regression steers an advantageous middle course between ordinary penalized quantile and expectile regressions without sacrificing their virtues too much when 1 < p < 2, that is, offers versatility and flexibility with these ‘quantile‐like’ and robustness properties. We develop the penalized L p ‐quantile regression with scad and adaptive lasso penalties. With properly chosen tuning parameters, we show that the proposed estimators display oracle properties. Numerical studies and real data analysis demonstrate the competitive performance of the proposed penalized L p ‐quantile regression when 1 < p < 2, and they combine the robustness properties of quantile regression with the efficiency of penalized expectile regression. These properties would be helpful for practitioners.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".