On Hotelling's Approach to Hypothesis Testing when a Nuisance Parameter is Present only under the Alternative
Bibliographic record
Abstract
In this paper we develop an alternative procedure to testing the significance of nonlinear terms in regression models based on the method of tubes. This statistical method was first introduced by Hotelling (1939) and has been recently extended by others in the statistics literature. The proposed procedure makes use of concepts from differential geometry and it can lead to an exact test with good power characteristics in certain circumstances. An earlier draft of this paper was presented at the CESG 1994 meeting in Windsor, Canada. The authors thank the participants for their helpful comments. Also comments from G. Fisher, T. Kariya and J. MacKinnon on the present version are gratefully acknowledged. The research of the first, second and fourth authors have been financially supported in part by SSHRC (Canada). The first author acknowledges the support of NSERC (Canada), while the third author acknowledges the support of NSF (USA). All authors gratefully acknowledge the financial suppo...
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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 | 0.035 | 0.058 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".