THE UNIVERSITY OF CALGARY Estimation of the Shape Parameter in the Elliptical Family of Distributions Based on Non–Parametric Measures of Association
Bibliographic record
Abstract
ii It is not so well known that there exist relationships between the correlation ρ (associ-ation parameter) of a bivariate normal population and some non–parametric measures of association such as Kendall’s tau and Spearman’s rho. These relationships are intro-duced for the two aforementioned measures along with Blomqvist’s quadrant measure of association. These relationships are not necessarily limited to the normal distribution and it is illustrated that for the family of elliptical distributions the relationship between Kendall’s tau or Blomqvist’s quadrant measure and the parameter ρ holds. Based on these relationships robust estimates of the association (correlation) param-eter are proposed. The properties of these estimates are investigated via simulation for various elliptical distributions in terms of bias, variance and root mean square error, and the robustness to extreme observations of these non–parametric estimates for the association parameter are discussed when a normal sample is contaminated with a few outliers.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".