Asymptotic independence in more than two dimensions and its implications on risk management
Bibliographic record
Abstract
Abstract In extreme value theory, the presence of asymptotic independence signifies that joint extreme events across multiple variables are unlikely. Although well understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of simultaneous occurrence of extremes in higher dimensions. In this article, we propose a notion of mutual asymptotic independence to capture the behaviour of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence . Additionally, we define ‐ wise asymptotic independence , which captures the tail dependence in between pairwise and mutual asymptotic independence. The concepts are compared using examples of Archimedean, Gaussian, and Marshall–Olkin copulas, among others. Finally, we discuss the implications of these new notions of asymptotic independence on assessing the risk in complex systems under distributional ambiguity.
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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 | 0.012 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".