Regression and correlation for 3 × 3 rotation matrices
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Bibliographic record
Abstract
Abstract This paper investigates a regression model for orthogonal matrices introduced by Prentice (1989). It focuses on the special case of 3 × 3 rotation matrices. The model under study expresses the dependent rotation matrix V as A 1 UA t 2 perturbed by experimental errors, where A 1 and A 2 are unknown 3 × 3 rotation matrices and U is an explanatory 3 × 3 rotation matrix. Several specifications for the errors in this regression model are proposed. The asymptotic distributions, as the sample size n becomes large or as the experimental errors become small, of the least squares estimators for A 1 and A 2 are derived. A new algorithm for calculating the least squares estimates of A 1 and A 2 is presented. The independence model is not a submodel of Prentice's regression model, thus the independence between the U and the V sample cannot be tested when fitting Prentice's model. To overcome this difficulty, permutation tests of independence are investigated. Examples dealing with postural variations of subjects performing a drilling task and with the calibration of a camera system for motion analysis using a magnetic tracking device illustrate the methodology of this paper.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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 it