Testing the symmetry of a dependence structure with a characteristic function
Bibliographic record
Abstract
Abstract This paper proposes competing procedures to the tests of symmetry for bivariate copulas of Genest, Nešlehová and Quessy (2012). To this end, the null hypothesis of symmetry is expressed in terms of the copula characteristic function that uniquely determines the copula of a given bivariate population with continuous marginal distributions. Then, test statistics based on L2 weighted distances computed from an empirical version of the copula characteristic function are proposed. Their asymptotic behavior is derived under the null hypothesis as well as under general alternatives. In particular, it is established that these rank statistics behave asymptotically as first-order degenerate V-statistics under the null hypothesis and this large-sample representation is exploited in order to provide suitably adapted multiplier bootstrap versions for the computation of p-values. The simulations that are reported show that the new tests are more powerful than the competing methods based on the empirical copula introduced by Genest, Nešlehová and Quessy (2012).
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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 | 0.118 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| 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".