Comparison of correlation-based measures of concordance in terms of asymptotic variance
Bibliographic record
Abstract
We compare measures of concordance that arise as Pearson's linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing distributions. The class of such transformed rank correlations includes Spearman's rho, Blomqvist's beta and van der Waerden's coefficient. When only the standard axioms of measures of concordance are required, it is not always clear which transformed rank correlation is most suitable to use. To address this question, we compare measures of concordance in terms of their best and worst asymptotic variances of some canonical estimators over a certain set of dependence structures. A simple criterion derived from this approach is that concordance-inducing distributions with smaller fourth moment are more preferable. In particular, we show that Blomqvist's beta is the optimal transformed rank correlation in this sense, and Spearman's rho outperforms van der Waerden's coefficient. Moreover, we find that Kendall's tau, although it is not a transformed rank correlation of that nature, shares a certain optimal structure with Blomqvist's beta.
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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 | 0.030 | 0.165 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".