A Vectorial Notion of Skewness and Its Use in Testing for Multivariate Symmetry
Bibliographic record
Abstract
By modifying the statistic of Malkovich and Afifi (1973 Malkovich , J. F. , Afifi , A. A. ( 1973 ). On tests for multivariate normality . J. Amer. Statist. Assoc. 68 : 176 – 179 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), we introduce and study the properties of a notion of multivariate skewness that provides both a magnitude and an overall direction for the skewness present in multivariate data. This notion leads to a test statistic for the nonparametric null hypothesis of multivariate symmetry. Under mild assumptions, we find the asymptotic distribution of the test statistic and evaluate, by simulation, the convergence of the finite sample size percentiles to their limits. We also present an associated test statistic for multivariate normality.
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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 | 0.016 | 0.079 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| 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".