Asymptotic Dependence for Light-Tailed Homothetic Densities
Bibliographic record
Abstract
Dependence between coordinate extremes is a key factor in any multivariate risk assessment. Hence, it is of interest to know whether the components of a given multivariate random vector exhibit asymptotic independence or asymptotic dependence. In the latter case the structure of the asymptotic dependence has to be clarified. In the multivariate setting it is common to have an explicit form of the density rather than the distribution function. In this paper we therefore give criteria for asymptotic dependence in terms of the density. We consider distributions with light tails and restrict attention to continuous unimodal densities defined on the whole space or on an open convex cone. For simplicity, the density is assumed to be homothetic : all level sets have the same shape. Balkema and Nolde (2010) contains conditions on the shape which guarantee asymptotic independence. The situation for asymptotic dependence, treated in the present paper, is more delicate.
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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 | 0.013 | 0.083 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".