Graphical and formal statistical tools for the symmetry of bivariate copulas
Bibliographic record
Abstract
Abstract Statistical tools to check whether the underlying copula of a pair of random variables is symmetric are developed. The proposed methods are based on the theoretical and empirical versions of the C‐power functions introduced and formally studied by Bahraoui & Quessy (2013). On one part, a methodology is developed for testing the null hypothesis that the copula of a given population is symmetric. To this end, a sequential testing procedure is proposed where at each level, the P‐value is estimated with the help of the multiplier bootstrap method. On another side, a related graphical method is proposed in order to gain an idea of the degree of asymmetry in bivariate data. The good properties of the methods in small samples are investigated with the help of Monte Carlo simulations under various scenarios of symmetric and asymmetric dependence. The newly introduced procedures are used to analyse the Nutrient and the Walker Lake data sets. The Canadian Journal of Statistics 41: 637–656; 2013 © 2013 Statistical Society of Canada
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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 | 0.017 | 0.100 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".