Composite bias‐reduced Lp‐quantile‐based estimators of extreme quantiles and expectiles
Bibliographic record
Abstract
Abstract Quantiles are a fundamental concept in extreme value theory. They can be obtained from a minimization framework using an asymmetric absolute error loss criterion. The companion notion of expectiles, based on asymmetric squared rather than asymmetric absolute error loss minimization, has received substantial attention from the fields of actuarial science, finance, and econometrics over the last decade. Quantiles and expectiles can be embedded in a common framework of ‐quantiles, whose extreme value properties have been explored very recently. Although this generalized notion of quantiles has shown potential for the estimation of extreme quantiles and expectiles, available estimators remain quite difficult to use: they suffer from substantial bias, and the question of the choice of the tuning parameter remains open. In this article, we work in a context of heavy tails and construct composite bias‐reduced estimators of extreme quantiles and expectiles based on ‐quantiles. We provide a discussion of the data‐driven choice of and of the anchor ‐quantile level in practice. The proposed methodology is compared with existing approaches on simulated data and real data.
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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 | 0.008 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".